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Дистанционная фотоплетизмография: теория и практика

Добрый день! Меня зовут Иван, я закончил медицинский институт как врач‑терапевт и в настоящее время учусь на 2-м курсе магистратуры МФТИ по направлению «Прикладной анализ данных в медицине». Я прохожу стажировку в Центре искусственного интеллекта в медицине в Лаборатории искусственного интеллекта в Сбере и хочу рассказать о своей работе в области дистанционной фотоплетизмографии. Настоящее исследование продолжает цикл статей о дистанционной фотоплетизмографии в Лаборатории искусственного интеллекта в Сбере [44].

Фотоплетизмография (ФПГ) — это диагностический метод, который позволяет оценить изменения объема крови в микрососудах из‑за сердечных сокращений и получить таким образом информацию о работе сердца и о состоянии сосудов.

Фотоплетизмография находит широкое применение в клинической практике — она лежит в основе пульсоксиметрии (измерении уровня кислорода в крови), используется для подсчета частоты дыхательных движений, оценки тонуса и жесткости сосудистой стенки при артериальной гипертонии, ишемической болезни сердца и заболеваниях периферических сосудов. Активно исследуется применение фотоплетизмографии для предсказания риска фибрилляции предсердий, сахарного диабета, обструктивного апноэ во сне и других заболеваний. Таким образом, фотоплетизмография может использоваться как для диагностики, так и для мониторинга различных витальных показателей [39, 40].

Классическая контактная фотоплетизмография основана на оптической денситометрии — определении оптической плотности ткани. Участок кожи, например, на пальце, освещается красным и инфракрасным светом, который после отражения или прохождения через ткань регистрируется сенсором. При этом наблюдаются пульсации света, отражающие пульсирующий характер кровотока в микрососудах. В зависимости от расположения источника и приемника светового сигнала различают два типа фотоплетизмографических сенсоров: 1) «на пропускание» (трансмиссионные сенсоры), когда источник и приемник расположены с противоположных сторон от объекта исследования, например, пальца; 2) «на отражение» (рефлективный сенсоры), когда источник и приемник расположены с одной стороны от объекта исследований (рис. 1) [2]. Пример получаемого пульсового сигнала приведен на рис. 2.

Рисунок 1 [40]. Контактная фотоплетизмография бывает трансмиссивная (а) и рефлективная (б).

Рисунок 2. Пример пульсового сигнала, получаемого при контактной фотоплетизмографии. Данные взяты из датасета UBFC-rPPG [37].

В последние годы в качестве альтернативы контактной фотоплетизмографии активно развивается дистанционная фотоплетизмография. Она основана на том, что изменение кровенаполнения мелких сосудов влияет на процесс отражения света [11]. Отраженный свет записывается видео‑камерой и анализ полученного видео позволяет выделить искомый пульсовой сигнал. При этом не требуется использование каких‑либо специальных сенсоров как в классической ФПГ.

Мы начнем с описания физиологических основ и алгоритмов дистанционной фотоплетизмографии, после чего обсудим ряд технических аспектов, влияющих на ее точность и эффективность. Последний раздел статьи посвящен проведенным экспериментам и их результатам.

1. Физиологические и алгоритмические основы дистанционной фотоплетизмографии

Дистанционная фотоплетизмография основана на том, что изменение кровенаполнения сосудов из‑за сердечных сокращений вызывает незначительные изменения окраски кожи. Данные изменения неразличимы для человеческого глаза, но могут быть проанализированы с помощью специальных алгоритмов для получения пульсового сигнала. Последний может быть использован для подсчета частоты сердечных сокращений или оценки вариабельности сердечного ритма.

Таким образом, в дистанционной ФПГ можно выделить несколько стандартных шагов, общих для всех классических алгоритмов обработки сигналов (рис. 3). Сначала на кадрах видеозаписи выбирается область интереса — лицо или его отдельный регион. Далее извлекается RGB‑сигнал — считается среднее значение RGB‑каналов в каждом кадре. Полученный RGB‑сигнал может дополнительно фильтроваться, а далее используется для извлечения пульсового сигнала с помощью одного из алгоритмов. Наконец, пульсовой сигнал фильтруется и на его основе производится подсчет частоты сердечных сокращений.

Рисунок 3. Стандартные этапы при дистанционной фотоплетизмографии: выбор области интереса, подсчет RGB-сигнала, применение одного из алгоритмов для получения пульсового сигнала, его фильтрация и подсчет частоты сердечных сокращений [30].

В настоящее время существует ряд методов обработки сигналов для дистанционной фотоплетизмографии. Мы опишем несколько из них, разберем преимущества и недостатки.

1.1. Метод Green

Цветовые каналы в RGB‑видео несут различную пульсовую информацию. Зеленый G‑канал содержит наиболее выраженный пульсовой компонент, так как (окси)‑гемоглобин в эритроцитах сильнее поглощает зеленый спектр по сравнению с красным. Кроме того, зеленый свет проникает глубже в кожу по сравнению с синим светом и таким образом лучше достигает сосудистого русла [3]. Результаты исследования на нескольких датасетах, показали, что наиболее информативным во всех случаях является G‑канал. На втором месте чаще всего находится B‑канал, а на третьем — R‑канал, однако в отдельных случаях разница между B‑ и R‑каналами не является статистически значимой [1]. Когда объем крови в сосуде возрастает, то большое количество гемоглобина поглощает больше света, поэтому отраженная часть света уменьшается, что и ведет к формированию пульсаций в сигнале [41].

Простейшая идея — это использовать G‑канал как наиболее информативный для определения пульса, что и было предложено в одном из первых методов дистанционной фотоплетизмографии, который получил название Green [3]. Первый этап, стандартный для большинства алгоритмов, состоит в пространственной нормализации. На каждом кадре в видео выбирается область интереса (лицо или отдельная его часть) и считается среднее значение G‑канала среди всех пикселей в данной области. Аналогичным образом проводится усреднение и двух других каналов, в методах, которые их используют. В методе Green сигнал из G‑канала фильтруется, чтобы оставить частоты в диапазоне соответствующем 40–240 ударам в минуту, после чего доминантная частота сигнала используется для оценки частоты пульса.

Однако, при таком подходе не учитывается информация, доступная в других каналах. Поэтому вслед за этим методом был предложен алгоритм G‑R, который дополнительно использует красный канал, вычитая его из зеленого [4]. Вычитание R‑канала оказывает положительный эффект, так как учитывает физиологическую информацию — G‑ и R‑каналы содержат максимальную и минимальную пульсовые амплитуды, поэтому их комбинация максимизирует пульсовой сигнал. Несмотря на свою простоту, данный метод показывает достаточно хорошие результаты (сравнение с другими методами приведено в разделе 3 в табл. 2).

1.2. Дихроматическая модель

Видимые изменения окраски кожи происходят согласно физиологическим особенностям отражения света от кожи, поэтому для лучшего понимания алгоритмов дистанционной фотоплетизмографии нам необходимо рассмотреть механизмы данного процесса. Согласно дихроматической модели при падении света на кожу одна его часть отражается непосредственно от поверхности кожи (зеркальное отражение), а другая — проникает в подлежащие ткани, где частично рассеивается, а частично, достигнув кровеносных сосудов, — отражается от них (диффузное отражение) [5, 11]. Описанный процесс схематично проиллюстрирован на рис. 4. Очевидно, что только диффузно отраженная часть светового потока содержит информацию о кровенаполнении сосудов и может использоваться для анализа пульса.

Рисунок 4. При падении света на кожу одна его часть отражается непосредственно от поверхности кожи (зеркальное отражение – specular reflection), а другая – проникает в подлежащие ткани, где частично рассеивается, а частично, достигнув кровеносных сосудов, – отражается от них (диффузное отражение – diffuse reflection) [5].

Световой поток, падающий на сенсор RGB-камеры, может быть представлен в виде зависимой от времени {(t)} функции:

$\begin{equation} C(t)=I_0 \cdot (1+i(t)) \cdot (u_c \cdot c_0 + u_s \cdot s(t) + u_p \cdot p(t)) \tag{1} \end{equation} ,$

где {C(t)} — это среднее значение RGB‑каналов в области интереса, {I(t)} — интенсивность светового потока, которая модулируется двумя компонентами — зеркальным отражением ${v_s(t)}$ и диффузным отражением ${v_d(t)}$ . Последний компонент ${v_n(t)}$ — это шумовой сигнал сенсора камеры. Однако мы делаем допущение, что благодаря относительному большому размеру области интереса шум камеры ${v_n(t)}$ является незначимым и может не учитываться. В отдельных областях зеркальное отражение может преобладать над диффузным. Но мы также делаем допущение, что благодаря эффективному выбору области интереса участки с доминирующим зеркальным отражением не рассматриваются.

Зеркальное отражение ${v_s(t)}$ изменяется при движениях, так как последние влияют на геометрические отношения между источником света, поверхностью кожи и камерой. Таким образом,

$\begin{equation} v_s(t)=u_s \cdot (s_0 + s(t)) \tag{2} \end{equation} ,$

где ${ u_s}$ – это спектр света, ${s_0}$ – стационарный компонент, а ${s_t}$ – компонент, зависимый от времени, а точнее говоря – от движений.

Диффузное отражение v_d(t) зависит от поглощения и рассеивания света в тканях под кожей и определяется в первую очередь постоянным уровнем меланина – пигмента, обуславливающим цвет кожи, и зависимым от времени (от кровенаполнения сосудов) уровнем гемоглобина. Таким образом,

$\begin{equation} v_d(t)=u_d \cdot d_0 + u_p \cdot p(t) \tag{3} \end{equation} ,$

где ${u_d}$ — постоянный компонент цвета кожи, d_0 — постоянный коэффициент отражения, ${u_p}$ — относительная сила пульсового сигнала в RGB каналах, а {p(t)} — непосредственно пульсовой сигнал.

Подставив {(2)} и {(3)} в {(1)} получим:

$\begin{equation} C(t)=I(t) \cdot (u_s \cdot (s_0 + s(t)) + u_d \cdot d_0 + u_p \cdot p(t)) \tag{4} \end{equation} ,$

Постоянные компоненты зеркального и диффузного отражений могут быть объединены в единый компонент:

$\begin{equation} u_c \cdot c_0 = u_s \cdot s_0 + u_d \cdot d_0 \tag{5} \end{equation} ,$

где ${u_c}$ – цвет отражаемого светового потока, а ${c_0}$ – сила отражения. Подставим {(5)} в {(4)} , получим:

$\begin{equation} C(t)=I_0 \cdot (1+i(t)) \cdot (u_c \cdot c_0 + u_s \cdot s(t) + u_p \cdot p(t)) \tag{6} \end{equation} ,$

где яркость светового потока {I(t)} также представлена в виде постоянного I_0 и зависимого от времени $I_0 \cdot i(t)$ компонентов.

В сигнале, получаемом из светового потока, условно различают две части – пульсирующую переменную часть {AC} , которая зависит от пульса, и непульсирующую медленно изменяющуюся часть {DC} , которая определяется медленным изменением кровенаполнения венозных и артериальных сосудов, а также изменением объема межклеточной жидкости и другими физиологическими процессами, влияющими на оптические свойства биологической ткани [2]. Раскрыв скобки в {(6)} , можно упростить выражение, так как компонент {AC} на порядок меньше компонента {DC} , и их произведения ${s(t) \cdot i(t)}$ и ${ p(t) \cdot i(t)}$ могут быть отброшены:

$\begin{equation} \begin{aligned} C(t) &= u_c \cdot I_0 \cdot c_0 + u_s \cdot I_0 \cdot s(t) + u_p \cdot I_0 \cdot p(t) + \\ &\quad + u_c \cdot I_0 \cdot c_0 \cdot i(t) + u_s \cdot I_0 \cdot s(t) \cdot i(t) + u_p \cdot I_0 \cdot p(t) \cdot i(t) \\ &\approx u_c \cdot I_0 \cdot c_0 + u_c \cdot I_0 \cdot i(t) + u_s \cdot I_0 \cdot s(t) + u_p \cdot I_0 \cdot p(t). \end{aligned} \tag{7} \end{equation}$

Для наглядности еще раз отметим роль отдельных компонентов в {(7)} :

$u_c \cdot I_0 \cdot c_0$ – это постоянная интенсивность света;

$u_c \cdot I_0 \cdot c_0 \cdot i(t)$ – это изменения интенсивности света, которые вызваны, главным образом, движениями;

$u_s \cdot I_0 \cdot s(t)$ – это компонент, связанный с зеркальным отражением света от поверхности кожи;

$u_p \cdot I_0 \cdot p(t)$ – это искомый пульсовой сигнал.

Таким образом, {C(t)} – это линейная комбинация сигналов, и ключевая задача алгоритма дистанционной фотоплетизмографии состоит в извлечении пульсового сигнала из {(7)} . Существующие методы можно разделить на две категории – основанные на слепом разделении сигнала (методы главных и независимых компонент) и учитывающие физиологические особенности процесса светоотражения. Мы начнем с рассмотрения алгоритма CHROM, который предоставит интуитивно понятную мотивацию для ряда ключевых концепций, используемых и в других алгоритмах.

1.3. Метод CHROM

Изменение амплитуды пульсового сигнала в каждом из RGB-каналов зависит от интенсивности источника света [12, 11]. Для того, чтобы устранить постоянное влияние интенсивности и цвета источника света на пульсовой сигнал следует выполнить временную нормализацию каждого из RGB-каналов – разделить сигнал ${C_i(t)}$ в каждом из каналов на среднее значение сигнала в канале за время ${\mu (C_i(t))}$ :

$\begin{equation} C_ni(t) = \frac {C_i(t)} { \mu (C_i(t))} \tag{8} \end{equation} .$

Нормализация во времени является одним из ключевых этапов алгоритмов, которые основаны на работе в нормализованном во времени RGB-пространстве. К таким алгоритмам относятся CHROM и POS.

Однако временная нормализация не может устранить влияние изменений интенсивности светового потока за период, во время которого проводится нормализации [12]. Подобные изменения обычно возникают из-за движений поверхности кожи относительно источника света. Предположив, что изменения интенсивности одинаковы для всех RGB-каналов, можно устранить их, взяв отношение двух нормализованных во времени RGB-каналов. Так как, как уже было отмечено, G- и R-каналы содержат максимальную и минимальную пульсовые амплитуды, можно взять их отношение, получив пульсовой сигнал, на который устранено влияние движений:

$\begin{equation} S = \frac {G_n(t)} { R_n(t)} -1 \tag{9} \end{equation} .$

Единица вычитается для приведения сигнала к виду, где среднее значение равно нулю. Недавно были также предложены методы GB и GRGB, в которых вместо отношения ${G_n(t) / R_n(t)}$ используются соответственно ${G_n(t) / B_n(t)}$ и ${G_n(t) / R_n(t)} + {G_n(t) / B_n(t)}$ [6].

Отношение двух каналов позволяет устранить влияние изменений интенсивности, но не может убрать влияние зеркального отражения от поверхности кожи. Отметим, что, в то время как диффузный компонент, несущий пульсовой сигнал, различен для RGB-каналов из-за особенностей абсорбции света тканями, зеркальный компонент, несущий шум, является одинаковым во всех RGB-каналах.

При использовании источника белого света зеркальный компонент привносит одинаковую фракцию белого света, которую можно устранить, используя разницу между цветовыми каналами, то есть цветность (chrominance). Из трех RGB-каналов можно получить два ортогональных сигнала цветности:

$\begin{equation} X=R-G, \\ Y=0,5R + 0,5G - B \tag{10} \end{equation} .$

При этом изменения, вызванные пульсовой волной, будут различаться для них, а изменения, вызванные движениями, будут одинаковыми. Используя описанный ранее подход {(9)}, можно взять их отношение, чтобы устранить влияние движений, получив пульсовой сигнал:

$\begin{equation} S = \frac {X_n} { Y_n } -1 = \frac {R-G} {0,5R+0,5G-B } -1 \tag{11} \end{equation} .$

Еще раз отметим смысл каждого из данных этапов:

1) временная нормализация {(8)} позволяет устранить влияние постоянного уровня интенсивности света ${(u_c \cdot I_0 \cdot c_0)}$ на пульсовой сигнал;

2) разница между цветовыми каналами позволяет устранить зеркальное отражение ${(u_s \cdot I_0 \cdot s(t))}$ , одинаковое во всех RGB каналах, получив в результате два сигнала цветности {(10)} ;

3) отношение двух сигналов цветности в {(11)} позволяет устранить влияние изменений интенсивности света из-за движений ${(u_c \cdot I_0 \cdot c_0 \cdot i(t))}$ .

Данный подход, однако, справедлив только при использовании источника белого света. Под источником света другого цвета алгоритм будет работать хуже. Для устранения означенного недостатка можно выполнить стандартизацию цвета кожи. В ходе эксперимента было установлено, что стандартизированный цвет кожи под источником белого света почти одинаков у всех людей:

$\begin{equation} u_{skin} = \frac {[R,G,B]} { \sqrt{R^2 + G^2 + B^2} } \tag{12} \end{equation} .$

Стандартизированный цвет кожи, конечно же, отличается в зависимости от цветотипа кожи (уровня меланина), однако различия невелики и потому пренебрежимы. Хотя более высокий уровень меланина усиливает абсолютное поглощение света кожей, поглощение света в разных RGB-каналах относительно друг друга остается почти одинаковым. Поэтому стандартизированный цвет кожи под источником белого света почти одинаков у всех людей [11].

Таким образом, для того чтобы выполнить поправку для источника света другого цвета, необходимо выполнить временную нормализацию каждого RGB-канала, используя {(8)} , а затем умножить на стандартизированный вектор цвета кожи {(12)} :

$\begin{equation} R_s=0,7682R_n,G_s=0,5121G_n,B_s=0,3841B_n \tag{13} \end{equation}.$

Далее подставим {(13)} в {(11)} :

$\begin{equation} S = \frac {X_s} { Y_s} -1 \tag{14} \end{equation} .$

$\begin{equation} \begin{aligned} X_s &= \frac{R_s - G_s}{0,7682 - 0,5121} = 3R_n - 2G_n, \\ Y_s &= \frac{R_s + G_s - 2B_s}{0,7682 + 0,5121 - 2 \cdot 0,3841} = 1,5R_n + G_n - 1,5B_n \end{aligned} \tag{15} \end{equation}$

Отметим, что изначально авторы в {(10)} выбрали {Y} как {Y=0,5R+0,5G-B} , однако в { (15) } , чтобы убрать дробные коэффициенты {0,5} , используют {Y=R+G-2B} . Очевидно, что результат будет тем же самым. Также отметим, что в {(10) } {X} представлен как {X=R-G} , a {Y} – как {Y=0,5R+0,5G-B} . Однако в { (15) } мы дополнительно добавляем знаменатели, для того чтобы вклад каждого из цветовых каналов имел корректный вес, соответствующий таковому при источнике света белого цвета. Мы можем расписать { (15) } чуть подробнее, чтобы увидеть, как получаются итоговые коэффициенты:

$\begin{equation} \begin{aligned} X_s &= \frac{R_s - G_s}{0{,}7682 - 0{,}5121} = \frac{0{,}7682R_n - 0{,}5121G_n}{0{,}7682 - 0{,}5121} \\ &= \frac{0{,}7682R_n - 0{,}5121G_n}{0{,}2561} \approx 2{,}999R_n - 1{,}999G_n \approx 3R_n - 2G_n. \end{aligned} \tag{16} \end{equation}$

Аналогичным образом:

$\begin{equation} \begin{aligned} Y_s & = \frac{R_s + G_s - 2B_s}{0,7682 + 0,5121 - 2 \cdot 0,3841} = \frac{0,7682R_n + 0,5121G_n - 2 \cdot 0,3841B_n}{0,7682 + 0,5121 - 2 \cdot 0,3841} \\ & = \frac{0,7682R_n + 0,5121G_n - 0,7682B_n}{0,7682 + 0,5121 - 0,7682} = \frac{0,7682R_n + 0,5121G_n - 0,7682B_n}{0,5121} \\ & \approx 1,500R_n + G_n - 1,500B_n \approx 1,5R_n + G_n - 1,5B_n. \end{aligned} \tag{17} \end{equation}$

Далее мы можем упростить {(14)} , используя свойства логарифмов и серию Тейлора:

$\begin{equation} log(1+s) = log(\frac {X_s} { Y_s} ) = log(X_s) - log(Y_s) \tag{18} \end{equation} ,$

$\begin{equation} log(x) = (x-1) - \frac {(x-1)^2} { 2)} + \frac {(x-1)^3} { 3)} -... \tag{19} \end{equation}$

Так как все аргументы логарифмов в {(18)} близки к единице, то

$\begin{equation} S≈X_s-Y_s=3R_n-2G_n-(1,5R_n+G_n-1,5B_n )=1,5R_n-3G_n+1,5B_n \tag{20} \end{equation} .$

Наконец, отметим, что амплитуда пульса {S} может быть сравнительно маленькой относительно ${X_s}$ и ${Y_s}$ . Если стандартизация цвета кожи окажется не совсем точной, то ${X_s}$ и ${Y_s}$ будут иметь разные амплитуды. Для коррекции можно использовать следующий механизм, называемый альфа-тюнингом:

$\begin{equation} S=X_s-αY_s,α= \frac {σ(X_s )} {σ(Y_s )} \tag{21} \end{equation} .$

Он обусловлен тем, что пульсовой сигнал находится в противофазе между ${X_s}$ и ${Y_s}$ , а искажения из-за изменений интенсивности светового потока при движениях находятся в фазе между ${X_s}$ и ${Y_s}$ . Таким образом, когда доминирует пульсовой компонент, то ${S_1}$ и ${S_2}$ находятся в противофазе, и поэтому их разность помогает усилить пульсовой сигнал. Если же доминируют искажения, обусловленные движениями, то разность их двух сигналов, находящихся в фазе, позволяет устранить данные искажения. Полученный алгоритм {(21)} основан на использовании двух сигналов цветности (chrominance), поэтому называется CHROM [12].

1.4. Методы слепого разделения сигнала

Метод главных компонент (PCA) и метод независимых компонент (ICA) [13, 14] позволяют разделить RGB сигнал {C(t)} на отдельные компоненты {Y(t)} , соответствующие интенсивности света, зеркальному отражению от кожи и диффузному отражению, несущему искомый пульсовой сигнал, с помощью матрицы {W} :

$\begin{equation} Y(t)=W·C(t) \tag{22} \end{equation} .$

Хотя алгоритмы слепого разделения сигналов на первый взгляд сильно отличаются от метода CHROM, отметим, что все они направлены на выделение пульсового сигнала как некой линейной комбинации сигналов из трех RGB-каналов. CHROM использует для этого постоянные во всех случаях коэффициенты в {(20)} :

$\begin{equation} S≈1,5R_n-3G_n+1,5B_n \tag{20} \end{equation} .$

a PCA и ICA – линейную комбинацию, определенную на основе {(22)} :

$\begin{equation} S=w_1 R_n-w_2 G_n+w_3 B_n \tag{23} \end{equation} .$

Разница между PCA и ICA заключается в их допущениях относительно указанных компонент: PCA предполагает, что они некоррелированные, а ICA – что они независимые. После разложения из {Y(t)} выбирается наиболее периодический сигнал как отражающий пульсовой компонент. Вследствие этого данные методы не работают, если движения человека также являются периодическими (например, при занятиях спортом). Более того другие частотные составляющие (например, дыхание) также затрудняют нахождение {W} [5]. Наконец, для корректного определения пульса необходимо использовать достаточно длинное видео (около 25 с), в то время как CHROM показывает хорошие результаты при работе и на значительно более коротких фрагментах [12]. Таким образом, благодаря учету особенностей физиологии и процесса отражения света CHROM демонстрирует лучшие результаты.

1.5. Временная нормализация и дихроматическая модель

Прежде чем перейти к описанию метода POS отметим более детально роль временной нормализации {(8)} в дихроматической модели {(7)} [5].

$\begin{equation} C(t) \approx u_c \cdot I_0 \cdot c_0 + u_c \cdot I_0 \cdot i(t) + u_s \cdot I_0 \cdot s(t) + u_p \cdot I_0 \cdot p(t) \tag{7}. \end{equation}$

Среднее во времени значение RGB-каналов ${\overline{C}(t) }$ отражает постоянный в течение определенного времени компонент светового потока: ${\overline{C}(t) \approx u_c \cdot I_0 \cdot c_0}$ , и может использоваться для временной нормализации исходного сигнала {C(t)} путем определения матрицы нормализации {N} , такой что

$\begin{equation} N \cdot \overline{C}(t) \approx u_c \cdot I_0 \cdot c_0 = 1. \tag{24} \end{equation}$

Таким образом, получим нормализованный во времени сигнал ${ C_n(t)}$ :

$\begin{equation} \begin{aligned} C_n(t) &= N \cdot C(t) \\ &= N \cdot u_c \cdot I_0 \cdot c_0 + N \cdot u_c \cdot I_0 \cdot c_0 \cdot i(t) + \\ &\quad+ N \cdot u_s \cdot I_0 \cdot s(t) + N \cdot u_p \cdot I_0 \cdot p(t) \\ &= 1 \cdot (1 + i(t)) + N \cdot u_s \cdot I_0 \cdot s(t) + N \cdot u_p \cdot I_0 \cdot p(t) \end{aligned} \tag{25} \end{equation}$

Отметим, что ${1 \cdot (1 + i(t))}$ — это изменение интенсивности света в направлении вектора {1} , который является вектором нормализованного во времени цвета кожи. Это наибольший компонент, изменения которого обусловлены движениями, и он одинаково представлен во всех RGB каналах. ${ N \cdot u_s \cdot I_0 \cdot s(t) }$ — это компонент зеркального отражения, а ${ N \cdot u_p \cdot I_0 \cdot p(t) }$ — это пульсовой сигнал.

Также приведем сигнал к форме, где среднее значение цвета равно нулю:

$\begin{equation} \tilde{C}_n(t) = C_n(t) - 1 = 1 \cdot i(t) + N \cdot u_s \cdot I_0 \cdot s(t) + N \cdot u_p \cdot I_0 \cdot p(t). \tag{26} \end{equation}$

1.6. Метод CHROM и дихроматическая модель

Перед обсуждением метода POS мы сделаем еще одно отступление и обсудим описанный ранее метод CHROM с позиций дихроматической модели [5]. Это позволит в дальнейшем подчеркнуть сходства и различия алгоритмов POS и CHROM, которые очень близки друг другу и отличаются, в сущности, лишь порядком выполняемых операций.

Метод CHROM работает в нормализованном во времени RGB-пространстве и состоит из двух ключевых и одного промежуточного этапов:

1) Проекция в направлении стандартизированного вектора цвета кожи под источником белого света ${u_{skin}}$ , чтобы выполнить поправку для источника света другого цвета. Данный этап является промежуточным так как необходим только в условиях освещения не соответствующих белому свету;

2) Проекция в ортогональную относительно зеркального отражения плоскость, чтобы устранить влияние зеркального отражения. В дихроматической модели {(26)} это – проекция ортогональная компоненту ${ (N \cdot u_s \cdot I_0 \cdot s(t)) }$ ;

3) Альфа-тюнинг для устранения искажений, вызываемых изменением интенсивности светового потока из-за движений.

Следуя описанию в [5], мы можем объединить первые два этапа в умножение на единую проекционную матрицу. На основе вектора ${u_{skin} = [0.7682; 0.5121; 0.3841]}$ создадим диагональную матрицу ${U_{skin}}$ , так что ${U_{skin}^{-1} \cdot u_{skin} = 1}$ :

$\begin{equation} U_{{skin}} = \begin{pmatrix} 0,7682 & 0 & 0 \\ 0 & 0,5121 & 0 \\ 0 & 0 & 0,3841 \end{pmatrix}. \tag{27} \end{equation}$

Матрица ${P_{Chrom}}$ для проекции в ортогональном относительно зеркального отражения направлении — это матрица коэффициентов, используемых для получения двух ортогональных сигнала цветности в {(10)} :

$\begin{equation} P_{{Chrom}} = \begin{pmatrix} 1 & -1 & 0 \\ 0,5 & 0,5 & -1 \end{pmatrix}. \tag{28} \end{equation}$

где строки соответствуют двум сигналам цветности, а столбцы – коэффициентам RGB-каналов. Умножим ${P_{{Chrom}}}$ и ${U_{skin}}$ :

$\begin{equation} \begin{aligned} P_{{Chrom}} \cdot U_{{skin}} &= \begin{pmatrix} 1 & -1 & 0 \\ 0.5 & 0.5 & -1 \end{pmatrix} \begin{pmatrix} 0,7682 & 0 & 0 \\ 0 & 0,5121 & 0 \\ 0 & 0 & 0,3841 \end{pmatrix} \\ &= \begin{pmatrix} 0,7682 & -0,5121 & 0 \\ 0,3841 & 0,2561 & -0.3841 \end{pmatrix}. \end{aligned} \tag{29} \end{equation}$

Чтобы показать эквивалентность полученной проекционной матрицы коэффициентам в оригинальной статье про CHROM выполним несколько простейших преобразований. Разделим каждую строку на наименьший по модулю ненулевой элемент:

$\begin{equation} \begin{aligned} \begin{pmatrix} \frac{0,7682}{0,5121} & -\frac{0,5121}{0,5121} & 0 \\ \frac{0,3841}{0,2561} & \frac{0,2561}{0,2561} & -\frac{0.3841}{0,2561} \end{pmatrix} &= \begin{pmatrix} 1,5 & -1 & 0 \\ 1,5 & 1 & -1,5 \end{pmatrix}. \end{aligned} \tag{30} \end{equation}$

Умножив первую строку на {2} , мы получим матрицу коэффициентов, как и в оригинальной статье:

$\begin{equation} \begin{aligned} \begin{pmatrix} 1,5 \cdot 2 & -1 \cdot 2 & 0 \\ 1,5 & 1 & -1,5 \end{pmatrix} = \begin{pmatrix} 3 & -2 & 0 \\ 1,5 & 1 & -1,5 \end{pmatrix}. \end{aligned} \tag{31} \end{equation}$

Возвращаясь к дихроматической модели {(26)} , рассмотрим результат проекции нормализованного во времени сигнала:

$\begin{equation} \tilde{C}_n(t) = C_n(t) - 1 = 1 \cdot i(t) + N \cdot u_s \cdot I_0 \cdot s(t) + N \cdot u_p \cdot I_0 \cdot p(t), \tag{26} \end{equation}$

$\begin{equation} S(t) = P_{{Chrom}} \cdot U_{{skin}} \cdot \tilde{C}_n(t) \approx P_{{Chrom}} \cdot U_{{skin}} \cdot 1 \cdot i(t) + P_{{Chrom}} \cdot U_{{skin}} \cdot N \cdot u_p \cdot I_0 \cdot p(t). \tag{32} \end{equation}$

Так как проекция является ортогональной относительно зеркального отражения ${(N \cdot u_s \cdot I_0 \cdot s(t))}$ , то ${ P_{{Chrom}} \cdot U_{{skin}} \cdot N \cdot \ u_s \cdot I_0 \cdot s(t)=0}$ , поэтому в {(32)} данный компонент исчезает.

Таким образом, мы получили два сигнала цветности {S(t)} , к которым далее применяется процедура альфа-тюнинга для устранения искажений, вызываемых изменением интенсивности светового потока из-за движений, то есть для устранения компонента ${1 \cdot i(t).}$

1.7. Метод POS

Наконец, мы обсудим State-of-the-art метод POS [5], который, как и CHROM, работает в нормализованном во времени RGB-пространстве, однако выполняет этапы проекции и альфа-тюнинга в обратном порядке.

1) Сначала устраняются искажения, вызываемые изменением интенсивности светового потока из-за движений, с помощью проекции в плоскость, ортогональную относительно направления интенсивности светового потока, то есть в направлении, ортогональном компоненту ${1 \cdot i(t)}$ . Данный компонент соответствует нормализованному оттенку кожи в дихроматической модели {(26)} . Поэтому получающая проекция – это проекция в плоскость, ортогональную нормализованному оттенку кожи. По этой причине метод POS и называется – метод проекции в плоскость, ортогональную оттенку кожи (Plane Orthogonal to Skin). Так как проекция является ортогональной относительно оттенка кожи, то нет необходимости выполнять поправку для источника света другого цвета. По этой причине в методе POS отсутствует этап умножения на стандартизированный вектор цвета кожи ${u_{skin}}$ .

При умножении на проекционную матрицу ${ P_{{POS}}}$ нормализованного во времени сигнала ${\tilde{C}_n(t) }$ получим согласно дихроматической модели {(26)} :

$\begin{equation} \tilde{C}_n(t) = C_n(t) - 1 = 1 \cdot i(t) + N \cdot u_s \cdot I_0 \cdot s(t) + N \cdot u_p \cdot I_0 \cdot p(t), \tag{26} \end{equation}$

$\begin{equation} S(t) = P_{{POS}} \cdot \tilde{C}_n(t) \approx P_{{POS}} \cdot N \cdot u_s \cdot I_0 \cdot s(t) + P_{{POS}} \cdot N \cdot u_p \cdot I_0 \cdot p(t). \tag{33} \end{equation}$

Так как проекция является ортогональной относительно интенсивности светового потока (или иначе говоря, нормализованного оттенка кожи) ${1 \cdot i(t)}$ , то ${ P_{POS} \cdot 1 \cdot i(t) = 0}$ . Поэтому данный компонент исчезает в {(33)} . Каким же образом мы можем выбрать проекционную матрицу ${ P_{POS}}$ ? Зависящий от времени компонент {i(t)} — это скаляр, поэтому он может изменить только длину вектора {1} , не влияя на его направление. Поэтому нам достаточно, чтобы ${ P_{POS} \cdot 1 = 0}$ . Нам также необходимо, чтобы оба компонента в ${ P_{POS}}$ — обозначаемые ${ P_{POS,1}}$ и ${ P_{POS,2}}$ — были ортогональны друг другу. Таким образом, необходимо, чтобы выполнялось два следующих условия:

$\begin{equation} \begin{aligned} &\begin{cases} \mathbf{P}_{{POS}} \cdot 1 = 0 \\ \mathbf{P}_{{POS},1} \cdot \mathbf{P}_{{POS},2} = 0 \end{cases} \end{aligned} \tag{34} \end{equation}$

Однако, каким же образом выбрать коэффициенты для проекционной матрицы? Существует много возможных вариантов. Для ответа на данный вопрос сделаем небольшое отступление.

Ранее в определенных стандартных условиях (галогеновая лампа в качестве источника света и камера UI-2220SE‑C для записи видео) было установлено, что в нормализованном во времени RGB‑пространстве вектор пульсового объема имеет стандартные значения [11]: ${u_{PBV}=[0.33, 0.77, 0.53]}$ . Данный вектор может использоваться напрямую для дальнейшего нахождения пульса, что лежит в основе другого алгоритма дистанционной фотоплетизмографии — PBV (Pulse Blood Volume). Такой подход обеспечивает высокую эффективность даже при существенных движениях человека. Однако его точность зависит от соответствия условий, при которых оценивается пульс, тем стандартным условиям, при которых был подсчитан данный вектор. В методе POS авторы использовали знание данного вектора для того, чтобы приблизительно оценить как выбранная проекционная матрица влияет на силу пульсового сигнала (рис. 5).

Рисунок 5. Нормализованные во времени RGB-сигналы проецируются в плоскость, ортогональную вектору (на рисунке – черная сплошная линия в трехмерном пространстве). Данный вектор указывает в направлении изменений интенсивности светового потока и при этом соответствует нормализованному оттенку кожи. В полученной плоскости показано распределение силы пульсового сигнала (красный / синий цвет соответствуют большой / меньшей силе сигнала). В зависимости от выбора проекционной матрицы проекция пульсового сигнала (вектора пульсового объема ) происходит в различные регионы плоскости. На рисунке приведены проекции для трех различных вариантов оси проекционной матрицы: , и . Их точечный продукт с позволяет оценить силу получаемого пульсового сигнала и соответствует , и . Правая часть рисунка показывает получаемый пульсовой сигнал. Очевидно, что проекция в направлении неудачна – полученный сигнал является зашумленным, что подтверждается низким по модулю значением силы пульсового сигнала [5].

Рисунок 5. Нормализованные во времени RGB-сигналы ${R_n(t), G_n(t), B_n(t)}$ проецируются в плоскость, ортогональную вектору {1}

(на рисунке – черная сплошная линия в трехмерном пространстве). Данный вектор указывает в направлении изменений интенсивности светового потока и при этом соответствует нормализованному оттенку кожи. В полученной плоскости показано распределение силы пульсового сигнала (красный / синий цвет соответствуют большой / меньшей силе сигнала). В зависимости от выбора проекционной матрицы проекция пульсового сигнала (вектора пульсового объема ${u_{PBV}=[0.33, 0.77, 0.53]}$ ) происходит в различные регионы плоскости. На рисунке приведены проекции ${ u_{PBV}}$ для трех различных вариантов оси проекционной матрицы: ${z_1=[-2, 1, 1]}$ , ${z_2=[1, -2, 1]}$ и ${z_3=[1, 1, -2]}$ . Их точечный продукт с ${ u_{PBV}}$ позволяет оценить силу получаемого пульсового сигнала и соответствует {−0,64}

. Правая часть рисунка показывает получаемый пульсовой сигнал. Очевидно, что проекция в направлении ${z_3}$ неудачна – полученный сигнал является зашумленным, что подтверждается низким по модулю значением силы пульсового сигнала {(−0.04)}

[5].

Оказалось, что сила получаемого пульсового сигнала зависит от того, в какую область плоскости, ортогональной оттенку кожи, происходит проекция пульсового сигнала. Поэтому проекционная матрица должна создаваться не произвольно, а с учетом указанных ранее физиологических особенностей — коэффициенты для RGB‑каналов берутся в порядке уменьшения пульсовой амплитуды. Напомним, что наибольшая амплитуда у G‑канала, а наименьшая — у R‑канала. Таким образом, авторы выбрали следующую проекционную матрицу

$\begin{equation} \mathbf{P}_{{POS}} = \begin{pmatrix} \mathbf{P}_{{POS},1} \\ \mathbf{P}_{{POS},2} \end{pmatrix} = \begin{pmatrix} 0 & 1 & -1 \\ -2 & 1 & 1 \end{pmatrix}. \tag{35} \end{equation}$

Мы можем убедиться, что оба условия в {(34)} действительно выполняются:

${P_{POS,1} \cdot 1=[0,1,-1]^T \cdot [1,1,1]=0 \cdot 1+1 \cdot 1-1 \cdot 1=0+1-1=0}$

${P_{POS,2} \cdot 1=[-2,1,1]^T \cdot [1,1,1]=-2 \cdot 1+1 \cdot 1+1 \cdot 1=-2+1+1=0}$

$\begin{equation} P_{POS,1} \cdot P_{POS,2} = [0,1,-1]^T \cdot [-2,1,1]=0 \cdot (-2)+1 \cdot 1-1 \cdot 1=0-1+1=0 \tag{36} \end{equation}$

При умножении на ${P_{POS}}$ полученные компоненты в {S(t)} эквивалентны следующим комбинациям RGB-каналов: ${S_1(t)=G_n-B_n, S_2(t)=-2R_n + G_n +B_n}$ . При этом оба компонента несут положительную пульсовую информацию, поэтому находятся в фазе.

2) Второй, и последний, этап POS — это альфа‑тюнинг для устранения зеркального отражения (напомним, что в методе CHROM альфа‑тюнинг используется для устранения искажений из‑за изменений интенсивности светового потока при движениях). Так как из‑за особенностей проекционной матрицы пульсовые компоненты в ${S_1}$ и ${S_2}$ находятся в фазе, то вместо их вычитания выполняется их сложение:

$\begin{equation} S = S_1 + \alpha S_2, \alpha = \frac{\sigma(S_1)} {\sigma(S_2)} \tag{37} \end{equation}$

Таким образом, когда доминирует пульсовой компонент, то ${S_2}$ и ${S_2}$ находятся в фазе и поэтому их сумма помогает усилить пульсовой сигнал. Если же доминируют находящиеся в противофазе искажения, вызванные зеркальным отражением, то разность их двух сигналов, позволяет устранить данные искажения.

Подводя итог, еще раз подчеркнем сходства и различия методов CHROM и POS в табл. 1. Два этапа — проекция и альфа‑тюнинг — выполняются в обратном порядке в данных методах, что и обуславливает их различия.

Таблица 1. Сравнительный анализ алгоритмов CHROM и POS

CHROM	POS
Временная нормализация для устранения влияния постоянного уровня интенсивности света ${(u_c \cdot I_0 \cdot c_0)}$	Временная нормализация для устранения влияния постоянного уровня интенсивности света ${(u_c \cdot I_0 \cdot c_0)}$
Проекция в направлении стандартизированного вектора цвета кожи под источником белого света	–
Проекция в плоскость, ортогональную зеркальному отражению, – позволяет убрать зеркальное отражение ${(u_s \cdot I_0 \cdot s(t))}$	Проекция в плоскость, ортогональную изменения интенсивности светового потока, –позволяет убрать искажения из-за изменения интенсивности светового потока из-за движений ${(1 \cdot i(t))}$
Альфа-тюнинг для устранения искажений из-за изменения интенсивности светового потока из-за движений ${(1 \cdot i(t))}$	Альфа-тюнинг для устранения зеркального отражения ${(u_s \cdot I_0 \cdot s(t))}$
Пульсовые компоненты находятся в противофазе	Пульсовые компоненты находятся в фазе

1.8. Метод OMIT

В заключение, мы рассмотрим метод OMIT, который был предложен в 2023 г. и основан на трансформации кадров с помощью ортогональной матрицы (Orthogonal Matrix Image Transformation). В данной работе авторы также разработали эффективный алгоритм для выбора области интереса, что позволяют улучшить результаты всех методов дистанционной фотоплетизмографии. Сам же метод OMIT является весьма простым с точки зрения мотивации и исполнения, однако несмотря на это является очень эффективным, в ряде случаев превосходя алгоритм POS.

Метод OMIT основан на разложении матрицы, содержащей средние значения RGB в каждом кадре видео, на ортогональные компоненты с помощью QR‑разложения. Матрица средних значений RGB-каналов в каждом кадре видео имеет форму ${n \times 3}$ , где {n} — число кадров, а {3} — средние значения трех RGB каналов. Данная матрица ${ A \in \mathbb{R}^{n \times 3} }$ может быть разложена на две другие матрицы — ${ Q \in \mathbb{R}^{n \times 3} }$ , которая содержит ортонормальный базис, и верхнюю треугольную матрицу ${ R \in \mathbb{R}^{3 \times 3} }$ , которая содержит коэффициенты, позволяющие представить оригинальную матрицу {A} в базисе {Q} . Таким образом,

$\begin{equation} A = Q R \tag{38}. \end{equation}$

Для эффективного разложения авторы используют метод отражений Хаусхолдера. В полученной матрице {Q} есть 3 столбца, которые образуют ортонормальный базис для исходной матрицы {A} . Ортонормальность означает, что векторы являются ортогональными друг другу и при этом их норма равна единице. Первый столбец ${q_1}$ в матрице {Q} показывает направление наиболее сильных изменений (наибольшей дисперсии) в исходном RGB пространстве. Данные изменения связаны в большинстве случаев с изменением цвета кожи при изменении интенсивности освещения из-за движений. Они также могут быть связаны с шумовым сигналом камеры или другими артефактами. Таким образом, означенное направление связано с факторами, которые затрудняют выявление пульсового сигнала. Для устранения влияния данных факторов выполняется проекция в направлении, ортогональном вектору ${q_1}$ .

Проекционная матрица ${P_{OMIT}}$ вычисляется следующим образом:

$\begin{equation} P_{OMIT} = I - q_1 q_2^T \tag{39}, \end{equation}$

где {I} — это единичная матрица размерностью ${n \times n}$ . Далее выполняется проекция исходной RGB-матрицы {A} и получается новая матрица {Y} :

$\begin{equation} Y = P_{OMIT} A \tag{40}. \end{equation}$

В полученной матрице {Y} первый столбец ${y_1}$ соответствует направлению наиболее сильных изменений, вызванных различным шумом, которые были устранены с помощью проекции. Тогда как второй столбец ${y_2}$ содержит искомый пульсовой сигнал после устранения шумового сигнала. Пульсовой сигнал ${(y_1)}$ после этого, как и в других методах, может быть дополнительно отфильтрован.

2. Технические аспекты дистанционной фотоплетизмографии

Описанные в прошлом разделе алгоритмы позволяют выделить пульсовой сигнал. Однако на их эффективность влияет целый ряд факторов, которые мы и обсудим в настоящей части.

2.1. Выбор области интереса

Первый этап при применении любого из алгоритмов дистанционной ФПГ — это выбор области интереса в видеозаписи [7]. Чаще всего для детекции лица используется алгоритм Виолы‑Джонса, который использует функцию Хаара и интегральное изображение для обнаружения и формирования прямоугольной рамки, ограничивающей лицо. Данный алгоритм отличается высокой скоростью, однако при его применении в области интереса остается часть фона. Более того, движения глаз, рта, блики от очков могут существенным образом влиять на подсчет пульса. Поэтому, исходя из стандартных пропорций человеческого лица, можно обрезать область интереса, исключив фон и глаза, и оставим только центральную часть лица или лоб. Более точный метод для детекции лица имплементирован в Mediapipe Face Mesh и позволяет детектировать 468 точек‑ориентиров на лице (рис. 6) [45]. Последние позволяют точным образом выделить лицо, убрав фон, убрать глаза и область рта или же выбрать отдельные участки, например часть лба или щек. Визуализация различных вариантов выбора области интереса приведена на рис. 7.

Рисунок 6. Mediapipe Face Mesh детектирует 468 точек-ориентиров на лице.

Рисунок 7. Сравнение методов выбора области интереса. Исходный кадр (а); прямоугольная рамка, ограничивающая лицо при применении алгоритма Виолы и Джонса (б); выбор центральной области рамки, чтобы убрать фон (в); закрытие области глаз для устранения влияния бликов (г); выделение лица с помощью точек ориентиров с помощью алгоритма Mediapipe Face Mesh (д); закрытие области глаз и рта с помощью точек ориентиров (е). Здесь и далее кадры взяты из датасета UBFC-rPPG для участников, которые подписали согласие на использование своих данных в статьях [37].

Выбор всего лица в качестве области интереса обеспечивает более стабильную оценку пульсового сигнала — за счет большей площади устраняется влияние шума в отдельных регионах. Однако при этом различные артефакты (очки, борода, усы и т. д.) могут затруднять точную оценку пульса. Более того, нужно отметить, что отдельные регионы лица отличаются друг от друга по интенсивности кровоснабжения и толщине эпидермиса, что напрямую влияет на процесс светоотражения. В связи с этим в литературе весьма популярен выбор лишь отдельных участков на лице. Сравнительный анализ показал, что наиболее перспективными являются области щек и лба, и именно данные регионы достаточно часто используются в качестве областей интереса в различных исследованиях [20].

Для выбора области интереса также возможно применение нейронных сетей, которые сегментируют изображение на отдельные части — фон, кожу, глаза, волосы и т. д. Так, в библиотеке pyVHR [31] используется модель для билатеральной сегментации BiSeNet [32] на основе ResNet18. Однако в ходе наших экспериментов при ее использовании качество сегментации оказалось низким. Более сложная модель SegFormer на основе архитектуры трансформера показала лучшие результаты [33]. Но обработка видео даже с использованием графического процессора в таком случае оказывается весьма медленной. Более того, модель оказалась неспособной убирать мелкие элементы, например бороду или усы, поэтому мы отказались от ее использования. Сравнение сегментации с помощью BiSeNet и SegFormer приведено на рис. 8.

Рисунок 8. Сегментация с помощью нейронных сетей. Исходный кадр (а). Сегментационная маска при использовании BiSeNet (б). Модель выделила фон, волосы, лицо, но оказалась неспособной на сегментацию очков и черт лица. Сегментационная маска при использовании SegFormer имеет значительно лучшее качество (в). Однако при ее применении к исходному кадру все еще сохранились борода и усы, что будет затруднять оценку пульсового сигнала (г).

Значительно более простым, но при этом более эффективным оказался подход на основе адаптивной оценки цвета кожи [34]. На первом этапе происходит выбор области лица, например с помощью алгоритма Виолы и Джонса, что позволяет убрать большое количество пикселей фона, оставив преимущественно пиксели кожи. Далее полученное изображение конвертируется в цветовое пространство HSV. В одном из каналов, происходит разбиение частоты пикселей различных цветов по гистограммам. Так как благодаря выбору области интереса большая часть пикселей фона была убрана, то доминирующим является цвет пикселей кожи, что и позволяет выбрать гистограмму с наибольшим числом пикселей ${hist_{max}}$ . После этого на основе эмпирически подобранного коэффициента ${\alpha}$ выбирается диапазон вокруг данной гистограммы с помощью следующей формулы:

${hist_{max} \pm (\alpha \cdot \frac { hist_{max} }{2})}$

Пиксели, имеющие цвет за пределами данного диапазона, не являются пикселями кожи и поэтому закрашиваются черным цветом. Данный подход отличается вычислительной простотой и позволяет эффективно убрать различные артефакты, затрудняющие оценку пульсового сигнала, — очки, волосы, бороду и усы. Результаты применения данного алгоритма приведены на рис. 9.

Рисунок 9 [34]. Применение метода гистограмм к различным каналам HSV пространства при различных значениях коэффициента ${\alpha}$ .

В ряде работ вместо выбора фиксированных регионов предлагается их динамическая оценка. Так, в [35] авторы предложили отслеживать 7 регионов, разделить каждый из них на небольшие квадраты, для каждого из полученных квадратов посчитать качество сигнала и затем найти пульсовой сигнал как среднее взвешенное всех сигналов, где вес выше у сигналов с лучшим качеством (рис. 10).

Рисунок 10 [35]. Отслеживание 7 регионов (а), их разделение на квадраты (б) и подсчет качества сигнала в каждом из квадратов (в).

Схожий подход был предложен и в [36], однако вместо отслеживания отдельных регионов выполнялось отслеживание всего лица. После оценки отношения сигнала к шуму для каждого из квадратов, выбирались лучшие из них и на их основе подсчитывался пульсовой сигнал (рис. 11).

Рисунок 11 [36]. Разделение кадров области интереса на квадраты (a), подсчет качества сигнала в каждом из квадратов (б) и выбор квадратов с наилучшим качеством.

В [37-38] авторы предложили использовать не фиксированное разбиение на квадраты, а на разделение на суперпиксели, отслеживаемые во времени, — темпоральные суперпиксели. Как и в других работах выбор оптимальных регионов выполнялся с помощью отношения сигнала к шуму (рис. 12).

Рисунок 12 [37]. Разделение кадров (а) на темпоральные суперпиксели (б) и оценка качества сигнала в каждом из квадратов них (в).

Авторы алгоритма OMIT предложили детальный подход для выбора области интереса, который позволил значительно улучшить эффективность всех алгоритмов дистанционной фотоплетизмографии [21]. На первом этапе определяется 85 точек‑ориентиров на лице. Они соединяются между собой, разделяя лицо на треугольники, которые затем проецируются в фиксированные координаты, соответствующие лицу человека во фронтальной проекции (рис. 13). Каждый кадр видео проецируется в данные фиксированные координаты, что позволяет измерять пульсовой сигнал в одних и тех же участках лица.

Рисунок 13 [21]. Определение точек ориентиров на лице (а), триангуляция по данным точкам (б) и проекция полученных треугольников в фиксированные координаты (в).

После проекции в фиксированные координаты производится разделение изображения на сравнительно крупные квадраты, в каждом из которых оценивается качество сигнала. Оценка пульса выполняется на основе квадратов с наилучшим сигналом (рис. 14).

Рисунок 14 [21]. В зависимости от положения лица в кадре и качества освещения выбирается 32 квадрата (сверху) или 20 квадратов (снизу).

Для оценки качества сигнала в каждом из регионов применяется следующий подход:

1) Проводится оценка дисперсии и исключаются регионы с нулевой дисперсией, как не несущие полезной информации.

2) Подсчитывается фрактальная размерность Катца — показатель, который оценивает степень иррегулярности сигнала и остроты пиков и характеризует насколько комплексным является характер сигнала. Далее находят отношение фрактальной размерности сигнала в одном регионе к фрактальной размерности глобального сигнала, полученного со всего лица, и выбираются регионы со значением >0,85 — это позволяет учитывать только те регионы, в которых сигнал имеют сопоставимые характеристики с глобальным сигналом. Таким образом, убираются регионы, несущие преимущественно шумовой сигнал.

3) Выполняется анализ детрендированных флуктуаций, который помогает оценить корреляцию между двумя нестационарными временными рядами. Данный метод позволяет проанализировать корреляцию между сигналом в отдельном регионе и глобальным регионом с помощью ‑экспоненты. Если ${\alpha=0,5}$ , то между временными рядами нет корреляции, если ${0,5< \alpha<1}$ — корреляция положительная, а если ${0< \alpha <0,5}$ , то корреляция отрицательная. Для дальнейшего анализы выбираются только регионы с положительной корреляцией.

После выбора регионов согласно означенным критериям, пульсовые сигналы из них суммируются во временном домене, позволяя получить итоговый пульсовой сигнал.

Наконец, в [22] авторы предложили оригинальный подход, основанный не на определении наилучших областей интереса, а на выборе оптимальных сигналов. Для этого они предложили отслеживать множество небольших регионов, определить в каждом из них пульсовой сигнал, а затем выполнить их спектральную кластеризацию, получив две группы. Сигналы с хорошим качеством имеют приблизительно одинаковый спектр и попадают в один кластер, тогда как сигналы с плохим качеством имеют большую внтуригрупповую (отличаются между собой) и межгрупповую (отличаются от сигналов в хорошем кластере) дисперсию. Итоговый пульсовой сигнал определяется на основе данных из хорошего кластера.

2.2. Применение фильтров

Одним из ключевых этапов является фильтрация полученного сигнала для устранения шума. При этом возможна как фильтрация RGB‑сигнала, так и полученного после применения одного из алгоритмов пульсового сигнала. Последний подход является более распространённым. Прежде всего используются классические фильтры для выбора частот в определенном диапазоне, соответствующем возможной частоте сердечных сокращений — от 40 до 240 ударов в минуту (0,75–3 Гц), а частоты ниже и выше данного диапазона исключаются. Чаще всего применяют фильтр Баттерворта, в отдельных работах — фильтра Чебышева 1 или 2 типа, фильтр Савицкого‑Голея, эллиптический фильтр, вейвлет‑фильтр и др., а также скользящий средний фильтр [9]. Сравнительный анализ указанных фильтров показал, что наиболее оптимальным является фильтр Чебышева 2 типа [9]. Для ЭКГ был предложен фильтр для устранения тренда [10], и он находит свое применение и в области дистанционной ФПГ. Результаты применения отдельных фильтров приведены на рис. 15.

Рисунок 15. Исходный пульсовой сигнал, полученный с помощью метода POS (a). Применение среднего скользящего фильтра для сглаживания сигнала (б). Применение фильтра для устранения тренда (в). Применение фильтра Чебышева 2 типа для сохранения частот в диапазоне 0,7-3 Гц (г).

Был также разработан ряд специальных фильтров, например, фильтр для выбора амплитуды [16]. Последний основан на том факте, относительная пульсовая амплитуда варьируется в определенном диапазоне, который может быть представлен как функция, зависимая от RGB‑каналов. В дальнейшем авторы предложили фильтр для фильтрации частот на основе искажений цветового сигнала [17], основанный на том факте, что пульсовой компонент и компоненты, связанные с изменением интенсивности и зеркальным отражением, имеют разные спектры отражения.

Наконец, существует ряд работ по применению методов машинного и глубокого обучения для фильтрации сигналов, например — использование метода опорных векторов [19] или нейронной сети долгой краткосрочной памяти для восстановления формы полученного пульсового сигнала [18].

Несмотря на большое число предложенных методов, сравнительно мало исследований посвящено сравнению эффективности различных фильтров и их комбинаций. В настоящей работе мы оценили эффективность ряда наиболее распространенных фильтров и их комбинаций для различных методов ФПГ.

2.3. Подсчет частоты сердечных сокращений

После получения пульсового сигнала проводят подсчет частоты сердечных сокращений (ЧСС) [7]. Наиболее распространенным является подход на основе спектрального анализа. Полученный сигнал конвертируется в частотный спектр с помощью быстрого преобразования Фурье или дискретного косинусного преобразования. Распределение спектральной плотности мощности (пример приведен на рис. 16) оценивается как функция частоты с помощью метода Велча в диапазоне от 0,7 до 3 Гц, что соответствует ЧСС от 40 до 180 ударов в минуту. Используемый диапазон в отдельных работах может немного различаться, например от 0,75 до 2,5 Гц (45 — 150 ударов в минуту). Частота с наибольшей мощностью {f} выбирается как соответствующая пульсовому сигналу и используется для подсчета ЧСС: ${ЧСС = 60 \cdot f}$ . Менее распространенным является поход на основе детекции пиков, соответствующих сокращениям сердца в полученном сигнале, и их подсчете.

Рисунок 16. Распределение спектральной плотности мощности для полученного пульсового сигнала (график голубого и оранжевого цвета). Отчетливо видны три доминантные частоты, соответствующие приблизительно 15, 75 и 600 ударам в минуту. После фильтрации частот в диапазоне от 0,75 до 2,5 Гц (от 45 до 150 ударов в минуту) остается только часть спектра (оранжевого цвета, ограничена вертикальными красными линиями), в которой наблюдается только одна доминантная частота, соответствующая 75 ударам в минуту.

2.4. Оценка результатов

Наиболее показательной метрикой является средняя абсолютная ошибка (MAE), показывающая абсолютную разницу между истинной ЧСС, определенной на основе ЭКГ или контактной ФПГ, и ЧСС по данной дистанционной ФПГ, усредненной по числу оцениваемых примеров: ${MAE = 1/N \cdot (|True HR - Estimated HR|)}$ . Во многих работах также применяется отношение сигнала к шуму для оценки информативности получаемого сигнала. Однако данная метрика, хотя и удобна для технического сравнения методов, не позволяет получить представление об их практической эффективности при оценке ЧСС. По этой причине мы сосредоточимся на использовании MAE.

Ключевым вопросом является методика оценки результатов. В одних работах для подсчета ЧСС используется все видео, а в других — видео разделяется на сегменты определенной длины, например по 5 или 10 секунд, и ЧСС определяется отдельно для каждого из сегментов, после чего метрика усредняется по всем сегментам. Более того, сегменты могут не пересекаться (например, 20-секундное видео можно разделить на 2 сегмента по 10 секунд), а могут идти с наложением (например с шагом в 1 секунду — в этом случае получится 11 сегментов). К сожалению, во многих работах авторы не указывают детали, что затрудняет возможность сравнения результатов [8]. Размер временного окна существенным образом влияет не только на оценку ЧСС с помощью дистанционной ФПГ, но и на истинную ЧСС, определяемую на основе ЭКГ или контактной ФПГ. Поэтому во всех случаях рекомендуется явно указывать данные параметры [15].

2.5. Альтернативные цветовые пространства

Для дистанционной ФПГ чаще всего используется RGB‑сигнал. Однако в ряде работ исследовались перспективы других цветовых пространств. Примеры трансформаций приведены на рис. 17. При сравнении 7 цветовых пространств — RGB, HSL, HSV, HIS, XYZ, YUV оказалось, что наиболее информативными были каналы Hue в HSL/HSV/HIS, Y в XYZ, U в YUV и G в RGB [23]. В другой работе при сравнении RGB, HSI, CIE Lab, YCrCb наиболее информативной оказалась комбинация Cr и Cb каналов в YCrCb [24]. Авторы также предложили модифицировать алгоритм POS, используя вместо комбинаций RGB сигналов, предложенных в оригинальной работе, Cr и Cb каналы. Трансформация из RGB в YCrCb пространство происходит следующим образом [25]:

$\begin{equation} \begin{aligned} \begin{pmatrix} Y \\ Cr \\ Cb \end{pmatrix} = \begin{pmatrix} 0.299 & 0.587 & 0.114 \\ -0.168 & -0.331 & 0.499 \\ 0.499 & -0.418 & -0.081 \end{pmatrix} \cdot \begin{pmatrix} R \\ G \\ B \end{pmatrix} \end{aligned} \end{equation}$

Поэтому в модифицированном POS оригинальная проекционная матрица была заменена на следующую:

${P = \begin{pmatrix} -0.168 & -0.331 & 0.499 \\ 0.499 & -0.418 & -0.081 \end{pmatrix} }$

Авторы отметили, что это повысило отношение сигнала к шуму в получаемом пульсовом сигнале, однако в ходе наших экспериментов абсолютная ошибка при использовании такого подхода оказалась большей по сравнению с оригинальным методом POS. В других работах было также отмечено преимущество использования HSI и YCrCb [26] и CIE Lab [27, 28] пространств по сравнению с RGB. Однако результаты являются противоречивыми. При непосредственном сравнении различных цветовых пространств наименьшая ошибка наблюдалась именно в RGB‑пространстве, тогда как использование HSI или YCrCb значительно ухудшало результаты [29]. В наших экспериментах цветовая трансформация в CIE Lab привела к некоторому улучшению результатов в датасете UBFC‑rPPG, однако для других датасетов это привело к увеличению ошибок.

Рисунок 17. Изображение в различных цветовых пространствах. Верхний ряд – RGB, CIE Lab, YCrCb. Нижний ряд – XYZ, HLS, HSV.

3. Экспериментальная часть и ее результаты

Настоящая работа была посвящена сравнению эффективности различных методов выбора области интереса и применения фильтров и их комбинаций для дистанционной фотоплетизмографии. Для анализа использовалось 3 датасета — UBFC‑rPPG (40 видео) [37], MCD‑rPPG (были выбраны 40 видео) и MMPD (было выбрано по одному видео для каждого из 33 участников) [43]. Каждое видео разделялось на непересекающиеся сегменты по 10 секунд, истинное значение ЧСС определялось на основе соответствующего сегмента контактной фотоплетизмограммы в датасете. Для подсчета ЧСС применялся спектральный анализ, а в качестве метрики использовалась средняя абсолютная ошибка.

Для выбора области интереса применялось несколько ранее описанных вариантов:

1) использование алгоритма Виолы и Джонса для получения области, содержащей лицо, и ее последующая обрезка для устранения краев, содержащих фон, а также закрытие области глаз для устранения влияния бликов;

2) использование Mediapipe Face Mesh для выбора всего лица за исключением глаз и рта;

3) использование Mediapipe Face Mesh для выбора области щек и лба;

4) использование алгоритма Виолы и Джонса для получения области, содержащей лицо, и применение адаптивной оценки цвета кожи с помощью гистограмм.

Третий вариант оказался наиболее эффективным. Сочетание третьего и четвертого вариантов, хотя и способствовало лучшей сегментации кадров, позволяя оставить только пиксели кожи, привело к незначительному ухудшению результатов.

Далее было проведено сравнение эффективности фильтра для устранения тренда, фильтра Баттерворта, фильтра Чебышева 2 типа и скользящего среднего фильтра [9] по отдельности, а также в комбинациях. Так как фильтры Баттерворта и Чебышева имеют схожую функцию, то их совместное применение не оценивалось. Таким образом было получено 12 возможных комбинаций фильтров, которые применялись совместно с алгоритмами GREEN, CHROM, POS, PBV, LGI и OMIT.

Использование оптимальной комбинации фильтров способно существенным образом улучшить эффективность дистанционной фотоплетизмографии. Лучшие результаты для каждого из алгоритмов, а также результаты без использования каких‑либо фильтров приведены в табл. 2. Отметим, что в датасете MMPD результаты значительно хуже из‑за сильного сжатия видео, что ведет к потере информации, затрудняя таким образом процесс извлечения пульсового сигнала.

Почти во всех случаях оптимальной комбинацией оказалось применение фильтра для устранения тренда и фильтра Чебышева 2 типа. Хотя данные фильтры давно известны, и фильтр Чебышева в сравнении с рядом других фильтров был показан как оптимальный [9], настоящий анализ показал, что они представляют собой оптимальную комбинацию.

Наиболее эффективным оказался метод POS, поэтому, чтобы детальнее показать влияние отдельных фильтров и их комбинаций приведем все результаты для данного метода в табл. 3. При этом ключевую роль играют частотные фильтры — их отсутствие (строки №9-12) сопровождается наихудшими результатами. Подтверждая данные литературы, отметим, что фильтр Чебышева 2-го (строки №1-4) типа эффективнее, чем более часто используемый фильтр Баттерворта (строки №5-8). Добавление фильтра для устранения тренда почти всегда ведет к улучшению результатов, тогда как скользящий средний фильтр в одних случаях показывает положительный, а в других случаях отрицательный эффект (например, при сравнении строк №1 и №3, №9 и №10, №11 и №12).

Для иллюстрации эффективности предложенной комбинации фильтров мы также приведем результаты из библиотеки rPPG‑Toolbox для дистанционной фотоплетизмографии [42]. В табл. 4 показано, что предложенная комбинация фильтров позволяет существенным образом улучшить результаты для всех алгоритмов дистанционной фотоплетизмографии.

Помимо алгоритмов дистанционной фотоплетизмографии, основанных на классических методах обработки сигналов, существуют также решения на основе глубокого обучения. Применение нейронных сетей для анализа видео позволяет добиться значительно более высокой точности. Однако серьезной проблемой является нестабильность получаемых результатов — модель, обученная на одном датасете может показывать существенно худшие метрики при тестировании на других наборах данных (сравнение результатов приведено в библиотеке rPPG‑Toolbox [42]). Ключевая причина — это, вероятно, небольшой размер датасетов для дистанционной фотоплетизмографии, что способствует сильному переобучению. Хотя в дальнейшем модели глубокого обучения могут оказаться более перспективными, в настоящий момент классические методы обработки сигналов благодаря своей устойчивости представляются более предпочтительными.

В заключение, отметим, что дистанционная фотоплетизмография — это активно развивающееся направление, которое имеет большие перспективы для использования в телемедицине, бесконтактном мониторинге жизненно важных показателей и в качестве скринингового метода диагностики благодаря простоте и удобству применения в сочетании с высокой точностью. Предложенная в настоящей работе комбинация фильтров, отличаясь простотой, может существенным образом улучшить работу алгоритмов извлечения пульсового сигнала и, таким образом, рекомендована для широкого применения с целью повышения эффективности методик дистанционной фотоплетизмографии.

Библиографический список

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I never imagined I would find myself in a situation where I was scammed out of such a significant amount of money, but it happened. I became a victim of a fake online donation project that cost me over $30,000. It all started innocently enough when I was searching for assistance after a devastating fire incident in California. While looking for support, I came across an advertisement that seemed to offer donations for fire victims. The ad appeared legitimate, and I reached out to the project manager to inquire about how to receive the donations. The manager was very convincing and insisted that in order to qualify for the donations, I needed to pay $30,000 upfront. In return, I was promised $1 million in donations. It sounded a bit too good to be true, but in my desperate situation, I made the mistake of believing it. The thought of receiving a substantial amount of help to rebuild after the fire clouded my judgment, and I went ahead and sent the money. However, after transferring the funds, the promised donations never arrived, and the manager disappeared. That’s when I realized I had been scammed. Feeling lost, helpless, and completely betrayed, I tried everything I could to contact the scammer, but all my efforts were in vain. Desperation led me to search for help online, hoping to find a way to recover my money and potentially track down the scammer. That’s when I stumbled upon several testimonies from others who had fallen victim to similar scams and had been helped by a company called Tech Cyber Force Recovery. I reached out to them immediately, providing all the details of the scam and the information I had gathered. To my immense relief, the experts at Tech Cyber Force Recovery acted swiftly. Within just 27 hours, they were able to locate the scammer and initiate the recovery process. Not only did they help me recover the $30,000 I had lost, but the most satisfying part was that the scammer was apprehended by local authorities in their region. Thanks to Tech Cyber Force Recovery, I was able to get my money back and hold the scammer accountable for their actions. I am incredibly grateful for their professionalism, expertise, and dedication to helping victims like me. If you have fallen victim to a scam or fraudulent activity, I highly recommend contacting Tech Cyber Force Recovery. They provide swift and efficient recovery assistance, and I can confidently say they made all the difference in my situation. ☎☎ 1️⃣5️⃣6️⃣1️⃣7️⃣2️⃣6️⃣3️⃣6️⃣9️⃣7️⃣ ☎☎ 📩 1️⃣5️⃣6️⃣1️⃣7️⃣2️⃣6️⃣3️⃣6️⃣9️⃣7️⃣ 📩
14.02.25 22:12 eunice49954

Agent Jasmine Lopez focuses on recovering stolen cryptocurrency, particularly USDT. She is well-known for helping victims of digital asset theft. Her reputation arises from successful recoveries that have allowed many to regain their lost funds. I witnessed this when $122,000 was taken from me. Thanks to Ms. Lopez's skills, I recovered the entire amount in just 24 hours. Her prompt response and effective methods relieved my financial burden. Ms. Lopez’s commitment to helping others is evident. She is always available to offer solutions to those facing similar problems. For assistance, she can be reached via email at recoveryfundprovider@gmail . com or contacted directly on WhatsApp and text at +44 - 7366 445035. Her Instagram handle is recoveryfundprovider.
15.02.25 02:51 Michelle Lynn

Living in Los Angeles, I never imagined I’d face such a difficult chapter in my life. At the time, my wife was pregnant, and we were both excited about starting a family. I fell victim to a series of scams, losing over $170,000 in total. Just when I thought things couldn’t get worse, I received a call from someone who promised to help me recover my losses. Desperate to fix the situation, I went along with it, hoping for a breakthrough. But it turned out to be another scam. However, most of the options I found either seemed dubious or offered no real guarantees. That’s when I came across Cyber Constable Intelligence. It was a company recommended in a Facebook community The team worked tirelessly on my case, and after some time, they successfully recovered 99% of my investment. Although I didn’t recover everything, the 99% recovery was a huge relief They also educated me on how to better protect my digital Asset Here's Their Website Info www cyberconstableintelligence com
15.02.25 02:51 Michelle Lynn

Living in Los Angeles, I never imagined I’d face such a difficult chapter in my life. At the time, my wife was pregnant, and we were both excited about starting a family. I fell victim to a series of scams, losing over $170,000 in total. Just when I thought things couldn’t get worse, I received a call from someone who promised to help me recover my losses. Desperate to fix the situation, I went along with it, hoping for a breakthrough. But it turned out to be another scam. However, most of the options I found either seemed dubious or offered no real guarantees. That’s when I came across Cyber Constable Intelligence. It was a company recommended in a Facebook community The team worked tirelessly on my case, and after some time, they successfully recovered 99% of my investment. Although I didn’t recover everything, the 99% recovery was a huge relief They also educated me on how to better protect my digital Asset Here's Their Website Info www cyberconstableintelligence com, WhatsApp Info: 1 (252) 378-7611
16.02.25 01:01 Peter

I fell victim to a crypto scam and lost a significant amount of money. What are the most effective strategies to recover my funds? I've heard about legal actions, contacting authorities, and hiring recovery experts, but I'm not sure where to start. Can you provide some guidance on the best ways to recover money lost in a crypto scam? Well if this is you, [email protected] gat you covered get in touch and thank me later
16.02.25 20:06 eunice49954

Agent Lopez specializes in recovering stolen cryptocurrencies, especially Bitcoin/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
18.02.25 19:35 donovancristina

Now, I’m that person sharing my success story on LinkedIn, telling others about the amazing team at TECH CYBER FORCE RECOVERY who literally saved my financial life. I’ve also become that guy who proudly shares advice like “Always back up your wallet, and if you don’t have TECH CYBER FORCE RECOVERY on speed dial.” So, a big thank you to TECH CYBER FORCE RECOVERY if I ever get a chance to meet the team, I might just offer to buy them a drink. They’ve earned it. FOR CRYPTO HIRING WEBSITE WWW://techcyberforcerecovery.com WHATSAPP : ⏩ wa.me/15617263697
18.02.25 22:13 keithphillip671

WhatsApp +44,7,4,9,3,5,1,3,3,8,5 Telegram @Franciscohack The day my son uncovered the truth—that the man I entrusted my hopes of wealth and companionship with through a cryptocurrency platform was a cunning scammer was the day my world crumbled. The staggering realization that I had been swindled out of 150,000.00 Euro worth of Bitcoin left me in a state of profound despair. As a 73-year-old grappling with loneliness, I had sought solace in what I believed to be a genuine connection, only to find deceit and betrayal. Countless sleepless nights were spent in tears, mourning not only the financial devastation but also the crushing blow to my trust. Attempts to verify the authenticity of our interactions were met with hostility, further deepening my sense of isolation. Through the loss it was my son who became my beacon of resilience. He took upon himself the arduous task of tracing the scam and seeking justice on my behalf. Through meticulous effort and determination, he unearthed {F R A N C I S C O H A C K}, renowned for their expertise in recovering funds lost to cryptocurrency scams. Entrusting them with screenshots and evidence of the fraudulent transactions, my son initiated the journey to reclaim what had been callously taken from me. {F R A N C I S C O H A C K} approached our plight with empathy and unwavering professionalism, immediately instilling a sense of confidence in their abilities. Despite my initial skepticism, their transparent communication and methodical approach reassured us throughout the recovery process. Regular updates on their progress and insights into their strategies provided much-needed reassurance and kept our hopes alive amid the uncertainty. Their commitment to transparency and client welfare was evident in every interaction, fostering a sense of partnership rather than mere service. Miraculously, in what felt like an eternity but was actually an impressively brief period, {F R A N C I S C O H A C K} delivered the astonishing news—I had recovered the entire 150,000.00 Euro worth of stolen Bitcoin. The flood of relief and disbelief was overwhelming, marking not just the restitution of financial losses but the restoration of my faith in justice. {F R A N C I S C O H A C K} proficiency in navigating the intricate landscape of blockchain technology and online fraud was nothing short of extraordinary. Their dedication to securing justice and restoring client confidence set them apart as more than just experts—they were steadfast allies in a fight against digital deceit. What resonated deeply with me {F R A N C I S C O H A C K} integrity and compassion. Despite the monumental recovery, they maintained transparency regarding their fees and ensured fairness in all dealings. Their proactive guidance on cybersecurity measures further underscored their commitment to safeguarding clients from future threats. It was clear that their mission extended beyond recovery—it encompassed education, prevention, and genuine advocacy for those ensnared by cyber fraud. ([email protected]) fills me with profound gratitude. They not only rescued my financial security but also provided invaluable emotional support during a time of profound vulnerability. To anyone navigating the aftermath of cryptocurrency fraud, I wholeheartedly endorse {F R A N C I S C O H A C K}. They epitomize integrity, expertise, and unwavering dedication to their clients' well-being. My experience with {F R A N C I S C O H A C K} transcended mere recovery—it was a transformative journey of resilience, restoration, and renewed hope in the face of adversity.
21.02.25 07:42 daniel231101

I never thought I would fall victim to a crypto scam until I was convinced of a crypto investment scam that saw me lose all my entire assets worth $487,000 to a crypto investment manager who convinced me I could earn more from my investment. I thought it was all gone for good but I kept looking for ways to get back my stolen crypto assets and finally came across Ethical Hack Recovery, a crypto recovery/spying company that has been very successful in the recovery of crypto for many other victims of crypto scams and people who lost access to their crypto. I’m truly grateful for their help as I was able to recover my stolen crypto assets and get my life back together. I highly recommend their services EMAIL ETHICALHACKERS009 AT @GMAIL DOT COM whatsapp +14106350697
21.02.25 21:38 eunice49954

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
22.02.25 18:01 benluna0991

Mark Zuckerberg. That’s the name I was introduced to when I first encountered the cryptocurrency mining platform, WHATS Invest. A person claiming to be Zuckerberg himself reached out to me, saying that he was personally backing the platform to help investors like me earn passive income. At first, I was skeptical—after all, how often do you get a direct connection to one of the world’s most famous tech entrepreneurs? But this individual seemed convincing and assured me that many people were already seeing substantial returns on their investments. He promised me a great opportunity to secure my financial future, so I decided to take the plunge and invest $10,000 into WHATS Invest. They told me that I could expect to see significant returns in just a few months, with payouts of at least $1,500 or more each month. I was excited, believing this would be my way out of financial struggles. However, as time passed, things didn’t go according to plan. Months went by, and I received very little communication. When I finally did receive a payout, it was nowhere near the $1,500 I was promised. Instead, I received just $200, barely 13% of what I had expected. Frustrated, I contacted the support team, but the responses were vague and unhelpful. No clear answers or solutions were offered, and my trust in the platform quickly started to erode. It became painfully clear that I wasn’t going to get anywhere with WHATS Invest, and I began to worry that my $10,000 might be lost for good. That's when I discovered Certified Recovery Services. Desperate to recover my funds, I decided to reach out to them for help. In just 24 hours, they worked tirelessly to recover the majority of my funds, successfully retrieving $8,500 85% of my initial investment. I couldn’t believe how quickly and efficiently they worked to get my money back. I’m extremely grateful for Certified Recovery Servicer's fast and professional service. Without them, I would have been left with a significant loss, and I would have had no idea how to move forward. If you find yourself in a similar situation with WHATS Invest or any other platform that isn’t delivering as promised, I highly recommend reaching out to Certified Recovery Services They were a lifesaver for me, helping me recover nearly all of my funds. It's reassuring to know that trustworthy services like this exist to help people when things go wrong. They also specialize in recovering money lost to online scams, so if you’ve fallen victim to such a scam, don’t hesitate to contact Certified Recovery Services they can help! Here's Their Info Below: WhatsApp: +1(740)258‑1417 mail: [email protected], [email protected] Website info; https://certifiedrecoveryservices.com
23.02.25 22:00 eunice49954

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
24.02.25 06:36 ANDREW DAVIS

RECOVER YOUR SCAMMED FUNDS AND CRYPTOCURRENCY VIA SPOTLIGHT RECOVERY Professional hackers at Spotlight Recovery provide services for compromised devices, accounts, and websites as well as for recovering stolen bitcoin and money from scams. They finish their work safely and quickly. Their order has been fulfilled since day one, and the victim will never be conscious of the outside entrance. Very few even attempt to give critical information, look into network security, or discreetly discuss personal issues. The Spotlight Recovery Crew helped me recover $264,000 that was stolen from my corporate bitcoin wallet, and I appreciate them giving me further details on the unidentified people. In the event that you have been defrauded of your hard-earned cash or bitcoins, contact SPOTLIGHT RECOVERY CREW at Contact: [email protected]
24.02.25 07:19 maggie4567

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
24.02.25 07:19 maggie4567

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
24.02.25 07:19 maggie4567

Jasmine Lopez specializes in recovering stolen cryptocurrencies, especially ETH/USDT. She has built a strong reputation for helping victims reclaim their lost funds. A personal example highlights her effectiveness: I lost $111,000 and, thanks to her prompt action, I recovered it all within 24 hours. Her dedication and skills eased my financial stress. She is always ready to assist others with similar issues. For help, she can be reached by email at Recoveryfundprovider@gmail. com or contact her through WhatsApp at +44 736 644 5035. Her Insta is recoveryfundprovider.
27.02.25 12:46 monikaguttmacher

Weddings are supposed to be magical, but the months leading up to mine were anything but. Already, wedding planning was a high-stress, sleep-deprived whirlwind: endless details to manage, from venue deposits and guest lists to dress fittings and vendor contracts. But nothing-and I mean, nothing-compared to the panic that washed over me when I realized that somehow, I had lost access to my Bitcoin wallet-with $600,000 inside. It happened in the worst possible way. In between juggling my to-do lists and trying to keep my sanity intact, I lost my seed phrase. I went through my apartment like a tornado, flipping through notebooks, checking every email, every file-nothing. I sat there in stunned silence, heart pounding, trying to process the fact that my entire savings, my security, and my financial future might have just vanished. In utter despair, I vented to my bridesmaid's group chat for some sympathetic words from the girls. Instead, one casually threw out a name that would change everything in a second: "Have you ever heard of Tech Cyber Force Recovery? They recovered Bitcoin for my cousin. You should call them." I had never heard of them before, but at that moment, I would have tried anything. I immediately looked them up, scoured reviews, and found story after story of people just like me—people who thought they had lost everything, only for Tech Cyber Force Recovery to pull off the impossible. That was all the convincing I needed. From the very first call, I knew I was in good hands. Their team was calm, professional, and incredibly knowledgeable. They explained the recovery process in a way that made sense, even through my stress-fogged brain. Every step of the way, they kept me informed, reassured me, and made me feel like this nightmare actually had a solution. And then, just a few days later, I got the message: "We have recovered your Bitcoin." (EMAIL. support @ tech cyber force recovery . com) OR WHATSAPP (+1 56 17 26 36 97) I could hardly believe my eyes: Six. Hundred. Thousand. Dollars. In my hands again. I let out my longest breath ever and almost cried, relieved. It felt like I woke up from a bad dream, but it was real, and Tech Cyber Force Recovery had done it. Because of them, I walked down the aisle not just as a bride, but as someone who had dodged financial catastrophe. Instead of spending my honeymoon stressing over lost funds, I got to actually enjoy it—knowing that my wallet, and my future, were secure. Would I refer to them? In a heartbeat. If you ever find yourself in that situation, please don't freak out, just call Tech Cyber Force Recovery. They really are the real deal.
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07.03.25 15:18 Ariduk

BEST LINK FOR RECOVERY SCAM ON TRADING INVESTMENT AND OTHERS TROUBLESHOOT? Welcome To General Hacking Techniques Service known as DHACKERS. Year 2025 we are active and best in what we do, as we give Solution to every problem concerning Web3 INTERNET activities, we guide you right to a positive fund Recovery e.t.c. Question From Most of Our Client, HOW POSSIBLE AND TIME WILL IT TAKE TO RECOVERY LOST OR SCAM FUND? Our Answer. Yes is 89.9% possible and how long it takes your Fund to be recovered depend on you. The fact is there are lot of fake binary investment companies out their, same a lot fake recovery companies and agents too. CAUTION 1). Make sure you ask one or two questions concerning the service and how they render there recovery services. 2) Do not give out your scammed details to any agent or hacker when you are not yet ready to recover back your fund. 3) do not make any payment when you are not sure of the service if you are to make one. (4) We discovered that most of this fake hacker or agent do give us scam details, playing the victim, because they can afford the service charge. 5) As long you have your scam details with you, you can recover your fund back anytime any-day with the right channel. Contact us from our Front Desk. [email protected] For advice and services, our standby Guru email. [email protected] [email protected] List of Service. ▶️Binary Recovery ▶️Data Recovery ▶️University Result Upgraded ▶️Clear your Internet Blunder and controversy ➡️Increase your Credit Score ➡️Wiping of Criminal Records ➡️Social Media Hack ➡️Blank ATM Card ➡️Load and wipe ➡️Phone Hacking ➡️Private Key Reset etc. For quick response. Email [email protected] Border us with your jobs and allow us give you positive result with our hacking skills. All Right Reserved (c)2025
08.03.25 04:42 andreassenhedda

If you’ve fallen victim to online scammers who have deceived you into investing your hard-earned money through fraudulent Bitcoin schemes, know that you're not alone. Countless individuals have been misled by scammers using various tactics to swindle money through deceptive investment platforms or promises of high returns. These scams often come in the form of fake cryptocurrency investments, Ponzi schemes, or phishing scams designed to steal your Bitcoin and other assets. Unfortunately, many victims suffer not only financial loss but also the psychological toll of realizing they’ve been taken advantage of. In some cases, scammers go even further, threatening legal consequences or using intimidation to keep victims silent. However, all hope is not lost. There are ways to recover your funds and potentially even bring those responsible to justice. One promising resource that can assist in reclaiming lost funds is Lee Ultimate Hacker, a trusted platform designed to help victims of online fraud. This service specializes in helping individuals who have been scammed through cryptocurrency investments or similar schemes. The platform’s expertise can help you navigate the process of recovering your money, giving you a chance to fight back against those who’ve wronged you. To begin the recovery process, it’s important to gather any proof of payment or transaction history involving the scammers. This evidence is crucial in tracing the flow of funds and identifying the scam operation behind it. Once you have collected your documentation, you can reach out to Lee Ultimate Hacker via LEEULTIMATEHACKER @ AOL . COM or wh@tsapp +1 (715) 314 - 9248 for assistance. They offer professional services to investigate fraudulent schemes, track Bitcoin transactions, and work to reverse fraudulent transfers. The recovery process can be complex and requires expert knowledge of blockchain technology and financial investigations, but with the help of a dedicated team, you’ll have a better chance of seeing your funds returned. In addition to helping you recover your assets, Lee Ultimate Hacker also works towards identifying the scammers and reporting them to the appropriate authorities. They understand the urgency of halting these fraudsters before they can victimize others. With their assistance, you not only increase the chances of recovering your funds but also play a part in holding cybercriminals accountable. If you've been affected by Bitcoin scams or other fraudulent online activities, reaching out to a service like Lee Ultimate Hacker can provide hope and a clear path forward. Their team can guide you through the recovery process, offering expert support while you take steps to reclaim what you’ve lost. It’s time to take action and work toward reclaiming your hard-earned money.
08.03.25 18:20 Diegolola514gmail.com

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08.03.25 18:23 faridasumadi

WEBSITE W.W.W.techcyberforcerecovery.com WHATSAPP +1 561.726.36.97 EMAIL [email protected] I Thought I Was Too Smart to Be Scammed, Until I Was. I'm an attorney, so precision and caution are second nature to me. My life is one of airtight contracts and triple-checking every single detail. I'm the one people come to for counsel. But none of that counted for anything on the day I lost $750,000 in Bitcoin to a scam. It started with what seemed like a normal email, polished, professional, with the same logo as my cryptocurrency exchange's support team. I was between client meetings, juggling calls and drafting agreements, when it arrived. The email warned of "suspicious activity" on my account. My heart pounding, I reacted reflexively. I clicked on the link. I entered my login credentials. I verified my wallet address. The reality hit me like a blow to the chest. My balance was zero seconds later. The screen went dim as horror roiled in my stomach. The Bitcoin I had worked so hard to accumulate over the years, stored for my retirement and my children's future, was gone. I felt embarrassed. Lawyers are supposed to outwit criminals, not get preyed on by them. Mortified, I asked a client, a cybersecurity specialist, for advice, expecting criticism. But he just suggested TECH CYBER FORCE RECOVERY. He assured me that they dealt with delicate situations like mine. I was confident from the first call that I was in good hands. They treated me with empathy and discretion by their staff, no patronizing lectures. They understood the sensitive nature of my business and assured me of complete confidentiality. Their forensic experts dove into blockchain analysis with attention to detail that rivaled my own legal work. They tracked the stolen money through a complex network of offshore wallets and cryptocurrency tumblers tech jargon that appeared right out of a spy thriller. Once they had identified the thieves, they initiated a blockchain reversal process, a cutting-edge method I was not even aware was possible. Three weeks of suffering later, my Bitcoin was back. Every Satoshi counted for. I sat in front of my desk, looking at the refilled balance, tears withheld. TECH CYBER FORCE RECOVERY not only restored my assets, they provided legal-grade documentation that empowered me to bring charges against the scammers. Today, I share my story with colleagues as a warning. Even the best minds get it. But when they do, it is nice to know the Wizards have your back.
09.03.25 17:22 Wayne707

‎Scammers have ruined the forex trading market, they have deceived many people with their fake promises on high returns. I learnt my lesson the hard way. I only pity people who still consider investing with them. Please try and make your researches, you will definitely come across better and reliable forex trading agencies that would help you yield profit and not ripping off your money. Also, if your money has been ripped-off by these scammers, you can report to a regulated crypto investigative unit who make use of software to get money back. If you encounter with some issue make sure you contact ( [email protected] ) they're recovery expert and a very professional one at that. ‎
10.03.25 18:18 springwilli

RECLAIM MY LOSSES REVIEWS HIRE DUNAMIS CYBER SOLUTIONI have always taken a security-first approach with my Bitcoin. That's why I put my hardware wallet in a fireproof safe-because you never know. Turned out I should have been even more paranoid. A few months ago, a fire took hold in my house. I lost nearly everything: the electronics, furniture, irreplaceable memorabilia. But when I dug through the remains, there it was: my Ledger hardware wallet, somehow intact. I held it up like some sort of post-apocalyptic movie scene, thinking, "At least my Bitcoin survived." But then, fate was not quite done with me: when I powered it on, it showed no signs of life whatsoever. The heat had fried the internal chip, and all I had was a melted, lifeless brick. That's when I realized my entire $680,000 in Bitcoin was trapped inside. At first, I told myself: "There has to be a way." From forensic data recovery to DIY repair tricks, everything I could conceivably Google, I researched. I considered buying an identical Ledger device and swapping components: spoiler, not a good idea unless you are an electrical engineer. Nothing worked. Every expert I contacted had the same answer: "Your Bitcoin is gone." I refused to accept that. That's when I found DUNAMIS CYBER SOLUTION I was skeptical, to say the least. If the manufacturer couldn't help me, how would they? At that point, I had no other choice but to try them. The first call I made, I immediately knew I was dealing with pros: no absurd promises, no giving of hopes, just explanation of their entire process with clarity-from advanced forensic techniques to secure data reconstruction. I mailed them my charred wallet, still half expecting a miracle to be impossible. Four days later, an email arrived. The subject line? "We have good news." They had successfully extracted my seed phrase and restored every single Bitcoin. I couldn't believe it. I had gone from losing everything to recovering $680,000 worth of crypto in just days. If your hardware wallet is damaged, dead, or seems irreparable, please do not give up. Just call DUNAMIS CYBER SOLUTION. They really did pull off some sort of high-stakes rescue operation on my behalf, and believe me, it was the stuff of legend. [email protected] +13433030545
10.03.25 20:19 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected]
10.03.25 20:19 wendytaylor015

My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected]
11.03.25 13:35 cristydavis101

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11.03.25 16:23 dannywilliams

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11.03.25 16:23 dannywilliams

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11.03.25 16:25 ricciordonez

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12.03.25 05:35 cholevasaca

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15.03.25 00:29 irenmroma

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15.03.25 14:34 spencerwerner

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17.03.25 12:20 browne

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17.03.25 13:14 vinnypraise

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17.03.25 15:23 Charlesagrimes

Running the small business was hard enough in itself without having to suffer such stress as loss of access to a Bitcoin wallet. I had put $532,000 into Bitcoin for my business in case of emergencies, but one day, the wallet was nowhere to be seen. I had trusted it to my friend while he managed my financials, little knowing he would prove less than trustworthy. I couldn't envision the gut-wrenching feeling coupled with a great feeling of folly for having placed so much trust in someone else's hands. I could not believe my eyes to see that all of my digital fortune was gone. Literally, every second of my busy day froze in disbelief as I tried to conceive the loss. I remembered the hours I had put into building my business, securing my investments, and planning for the future. Now, I was staring at an empty wallet that once held my safety net. This hit me hard-not only had I lost $532,000, but the betrayal hurt further because it came from someone I considered reliable. The emotional toll was huge, and this financial hit could cripple my business. In the midst of my despair, I knew I had to act fast. I went online, searching everywhere for a solution through which I could get back in control of my finances. That is where I came across Digital resolution services. I knew them for recovery related to lost crypto, but also somehow skeptical. At that point, it looked like I had nothing left to lose. I reached out, and with our very first conversation, I gained the impression that they did understand my situation. Their team was nothing short of extraordinary. They approached my case with professionalism and empathy, meticulously explaining the recovery process in clear, simple terms that alleviated some of my anxiety. They set realistic expectations while promising to do everything possible to retrieve my funds. Over the next several weeks, they worked tirelessly, employing advanced blockchain forensic techniques and sophisticated tracking tools that I’d never even heard of before. It kept me informed with constant updates and gave me hope in this desperate time. Finally, it came-the day Digital resolution services recovered my lost Bitcoin. Relief overwhelmed me, and it wasn't all about the money but control and self-trust in my financial future. This experience taught me the most valuable lesson: never lose control over your own financial security and never put blind trust in anyone. With Digital resolution services, I recovered not only my $532,000 but also learned how to protect my assets better in the future. Contact Digital Resolution Services: Email: digitalresolutionservices (@) myself. c o m WhatsApp: +1 (361) 260-8628 Stay protected Charles agrimes
18.03.25 23:49 lindaspringer311

My name is Linda Springer, and I am part of an ultra-high-net-worth family in the United Kingdom. Managing our wealth has always been a top priority, and I’ve always looked for opportunities to grow and diversify our investments. When I was introduced to an offshore banking investment program called Market Fund, it seemed like the perfect opportunity to enhance our portfolio. The program promised impressive returns, and with professional advisors and seemingly legitimate documentation, I felt confident that it was a secure investment. However, my trust in Market Fund quickly proved to be misplaced. Initially, everything seemed to go smoothly. Reports showed strong growth, and I was reassured by the continuous updates from the program’s advisors. But when I tried to withdraw my funds, everything took a sharp turn. The Market Fund website became unresponsive, and all my attempts to reach the advisors through emails and phone calls went unanswered. It was then that I realized I had fallen victim to a scam, and the £60,000 I had invested was gone. Feeling devastated and unsure of what to do next, I turned to a friend I had met at a club called The Vault. During one of our conversations, Alex, a fellow club-goer, mentioned how Rapid Digital Recovery had helped them recover funds from a similar fraudulent scheme. Intrigued by their success story, I decided to reach out to Rapid Digital Recovery....Whatsapp: +1 4 14 80 71 4 85.. hoping they could help me recover my money as well. From the moment I contacted them, the team at Rapid Digital Recovery took immediate action. They began investigating the scam and used advanced technology to trace the origins of Market Fund. Through their efforts, they uncovered a network of fake websites and shell companies that had been designed to deceive investors like myself. Thanks to their persistence and expertise, Rapid Digital Recovery successfully recovered the £60,000 I had lost.....Email: rapid digital recovery (@) execs. com.. Not only did they restore my financial security, but they also exposed the fraudulent operation behind Market Fund, preventing others from falling victim to the same scam. While the experience was incredibly stressful, it served as an important reminder of the need for due diligence and professional oversight when dealing with offshore investments. I am incredibly grateful to Rapid Digital Recovery for their support, expertise, and determination in recovering my funds. Telegram: h t t p s: // t. me /Rapiddigitalrecovery1
20.03.25 17:21 katherineingram

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20.03.25 17:21 katherineingram

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20.03.25 19:34 ysabelbristol

I am YSABEL, a medical student living with my grandmother. For the past few years, I’ve been diligently saving my grandmother’s money to ensure she has a comfortable and secure future. I invested over $40,000 into an online platform, which promised significant returns. After completing several steps, they told me that to withdraw the money, I needed to make another payment of $73,000. As a medical student, my time is already stretched thin, and managing my grandmother’s finances on top of my studies was overwhelming. That's when a costudent, who had gone through a similar experience, recommended MUYERN TRUST HACKER. Initially, I was skeptical. After all, how could anyone help me recover the money I had already lost to such a sophisticated scam? But after reaching out to them, I quickly realized I was in good hands. From the very first conversation, the team at MUYERN TRUST HACKER was professional, compassionate, and knowledgeable. They understood the gravity of my situation and took the time to thoroughly review all the details of my case. They explained the recovery process clearly, step by step, and assured me that they would work tirelessly to help recover the funds I had lost. Their expertise in dealing with online fraud was evident, and for the first time in weeks, I felt a sense of hope that I could regain control over this situation. The recovery process wasn’t immediate, and there were moments of uncertainty, but MUYERN TRUST HACKER remained dedicated and persistent. As someone who has been working hard to save and protect my grandmother’s money, it was devastating to feel like I might lose everything to a scam. But MUYERN TRUST HACKER gave me the support, expertise, and guidance I needed to recover what was lost. I’m deeply grateful for their help, and I now have a renewed sense of hope that I can protect my grandmother’s future. If you find yourself in a similar situation, feeling trapped and overwhelmed by a fraudulent company, I highly recommend MUYERN TRUST HACKER. (Whats A p p at + 1 (440) (335) (0205) Their team provides real solutions, and their professionalism and dedication were a lifeline for me during a very difficult time. Thanks to them, I feel confident that I can move forward and continue to protect my grandmother’s savings. Alternatively, contact their tele gram also if you need immediate attention at muyerntrusthackertech.
21.03.25 21:19 carmenbeechum643

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22.03.25 14:13 [email protected]

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23.03.25 12:24 maryjul75

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23.03.25 22:01 joaneldnde

The ground trembled like a nervous intern on espresso shots. One minute, I was monitoring my geothermal Bitcoin miners, humming in harmony with Iceland's most unpredictable volcano. Next? An eruption painted the sky gray with ash, raining destruction like an out-of-control blockchain fork. Power cables flickered out. Servers turned into abstract-art pieces. And my wallet with $460,000 worth of mining revenue fried faster than a motherboard in a tidal wave of lava. I was knee-deep in volcanic mud, clutching the charred wallet, wondering if the universe had a vendetta against renewable energy. For weeks, I’d played geothermal gambler, harnessing Earth’s anger to mine crypto. Now, Mother Nature had countered with a literal power move. My wallet’s backups? Corrupted by ash-clogged drives. My cold storage? Warmer than a freshly erupted fissure. Even the volcanologists on my team shrugged. “We predict lava, not ledger errors,” one said, handing me a business card signed at the edges. “Try these Cyber Constable Intelligence. They’ve fixed crypto in weird places.” Cyber Constable Intelligence phoned on the first ring. Cyber Constable Intelligence saved not just crypto. They demonstrated that even the fury of nature cannot surpass human tenacity. My operation now operates robustly, excavating coins with Earth's anger and a backup generator sufficient to run a small glacier. The volcano? Still grumbling. My wallet? Locked inside a fireproof safe, as irony bites sharper than an Icelandic winter. If your crypto somehow gets smothered beneath the pyroclastic ash of life, skip the freak-out. Call the Cybers. They'll dig through lava streams until your cash bubbles up to the surface. Just maybe set up your rigs a few miles closer to the crater next time. If you’re facing a similar problem I highly recommend contacting Cyber Constable Intelligence 📞 WhatsApp:+1 (2 5 2 ) 3 7 8 7 6 1 1 🌐 Website: www cyberconstableintelligence.com 📩 Telegram: https://t.me/cyberconstable
23.03.25 22:18 [email protected]

A few months ago, I stumbled upon a post about a cryptocurrency investment platform that I thought was a good idea for me to invest in crypto, I didn’t realize I was being catfished by the cryptocurrency investment manager who promised me huge returns on my investment. I lost my capital of $170,000 and interest without receiving any profits in return, I was devastated And I realized I had been scammed out of my cryptocurrency. I felt hopeless and didn’t know where to turn. i searched everywhere for a solution and That’s when my friend introduced me to a Crypto recovery platform Trust Geeks Hack Expert. At first, I was skeptical—after all, I had just been scammed—but Trust Geeks Hack Expert professionalism and transparency reassured me. They took the time to analyze my case, track my lost funds, and guide me through the recovery process. To my amazement, they successfully retrieved my stolen crypto! I can’t express how grateful I am to Trust Geeks Hack Expert team. Their expertise and dedication gave me a second chance. If you’ve been a victim of a crypto scam, don’t lose hope—Trust Geeks Hack Expert. is the real deal! for assistance, Email: [email protected] (TeleGram:: Trustgeekshackexpert) & what's A p p +1 7 1 9 4 9 2 2 6 9 3
24.03.25 10:03 Diegolola514gmail.com

"I am incredibly grateful to Sylvester Bryant for his exceptional expertise and assistance in recovering my USDC funds, which were lost to a phishing scam. Thanks to his diligent efforts, he successfully retrieved €480,000 worth of USDC that I thought was gone forever. If you or anyone you know has fallen victim to a similar situation, I highly recommend reaching out to Sylvester for professional assistance. You can contact him via email at Yt7cracker@gmail. com or through WhatsApp/text message at +1 512 577 7957. He is truly a reliable and skilled professional in recovering assets from online scams."
25.03.25 18:06 maryjul75

Fast Agent Recovery is a consulting firm that specializes in the recovery of assets from financial fraud. We know how to recover your funds and we have helped thousands of scam victims from around the world to recover their money. If you are a victim of Binary Options fraud, Forex fraud, Bitcoin fraud, Dating scams or one of the many other the online fraudulent practices that permeate the internet then file a complaint on www.fastrecoveryagent,.com to get an assessment if we can help you get your money back too. File a complaint: https://www.fastrecoveryagent.com/
27.03.25 01:52 debrapavon89

The moment my cold storage device flatlined, erasing $385,000 in Bitcoin I’d saved to launch a chain of zero-waste cafés, I became a ghost haunting my own life. I scrolled through forums until my eyes were streaming, trawling through threads filled with such mouthfuls as "irreversible blockchain entropy" and "cryptographic oblivion A Reddit thread finally revealed to me Cyber Constable Intelligence I reached out, the team at Cyber Constable Intelligence took immediate action. They began tracing the fraudulent car auction site and thoroughly investigating the scam. To my relief, after several weeks of hard work, Cyber Constable Intelligence successfully tracked down the scammers and recovered the full $385,000 I had lost. Their hard work allowed me to move on from this unfortunate experience, I highly recommend their services to anyone who has been affected by online fraud Reach out to their Info below WhatsApp: 1 252378-7611 Website info; www.cyberconstableintelligence.com
30.03.25 03:25 orrinharber

The ad on X (formerly Twitter) popped up on my timeline one lazy Sunday afternoon. It was flashy, bold, and impossible to ignore. The headline read, “ONCE-IN-A-LIFETIME COMEDY EXTRAVAGANZA!” with a dazzling graphic of a stage lit up in neon lights. The caption said: “Kevin Hart, Ali Wong, Dave Chappelle, and a MYSTERY LEGENDARY COMEDIAN live in Vegas! Limited VIP tickets available. Don’t miss out!” The post had thousands of likes, retweets, and comments like, “This is going to be epic!” and “Already got my ticket!” It even had a blue checkmark next to the account name, which made it seem legit. I clicked the link, and it took me to a sleek website with a countdown timer and a list of sold-out ticket tiers. The only option left was a $125,000 VIP package, which promised front-row seats, backstage access, and a meet-and-greet with the comedians. I hesitated for a moment, but the fear of missing out got the better of me. I thought, When will I ever get a chance like this again? So, I entered my credit card details and hit “Purchase.” The confirmation email came through instantly, and I felt a rush of excitement. Little did I know, I’d just fallen for one of the most elaborate scams I’d ever encountered. Looking back, I should’ve noticed the red flags the overly pushy tone of the ad, the lack of reviews for the event, and the fact that no official accounts from the comedians promoted it. But in the moment, it all seemed so real.I had been swept up by the flashy ad, the excitement of the event, and the FOMO (fear of missing out) that made it seem like an opportunity I couldn’t let slip by. Everything about the ad screamed “exclusive” and “once-in-a-lifetime,” which was enough to convince me to take the plunge. Yet, as time went on and I tried to follow up on the event, I found there was no trace of it anywhere. There were no details, no event pages, and no mention from the comedians themselves. My heart sank as I realized I had been scammed.Thankfully, GRAYWARE TECH SERVICES helped me get my money back, but the experience was a hard lesson in online scams. I’ll never forget that ad on X the one that cost me $125,000 and a whole lot of pride. I learned the importance of being cautious online, checking for reviews, and looking for signs of authenticity before jumping into anything that seems too good to be true.You can reach GRAYWARE TECH SERVICES on web at ( https://graywaretechservices.com/ ) also on Mail: ([email protected])
30.03.25 06:22 grace111

I recommend Marie ([email protected] and WhatsApp: +1 7127594675) for recovering lost or stolen bitcoin, USDT, or any other cryptocurrency from fraudulent investment sites because they are very knowledgeable in the industry and will reimburse all of your money. I can say with confidence that she was the only one who was able to credit my account with $52,760 of the money that had gone missing, based on my prior transactions with them. She was the only one who could. Since they are the only ones that can fully return your missing funds to your account without any deductions, I sincerely appreciate their job and am recommending her to you today.
31.03.25 11:00 maryjul75

Fast Agent Recovery is a consulting firm that specializes in the recovery of assets from financial fraud. We know how to recover your funds and we have helped thousands of scam victims from around the world to recover their money. If you are a victim of Binary Options fraud, Forex fraud, Bitcoin fraud, Dating scams or one of the many other the online fraudulent practices that permeate the internet then file a complaint on www.fastrecoveryagent,.com to get an assessment if we can help you get your money back too. File a complaint: https://www.fastrecoveryagent.com/
02.04.25 23:16 frederickhandy

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02.04.25 23:18 frederickhandy

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03.04.25 07:57 messijohn

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03.04.25 10:58 elizabethrush89

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03.04.25 10:58 elizabethrush89

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04.04.25 09:49 mkihn634

When my $870,000 Bitcoin investment was trapped in the crumbling ruins of an offshore exchange, I felt as if my financial future had been buried at sea. It was meant to be my safety net, a shield against life’s uncertainties, but now it seemed like nothing more than a digital ghost. Each news update about the exchange's insolvency hit me like a tidal wave, dragging my hope under. It was a sleepless night, scanning through horror stories in forums as other people were losing everything. I could see my dreams flying out the window. That is until a former client, who had weathered a similar storm, said GRAYWARE TECH SERVICES in a hushed but confident tone. "They are the best there is," he said. "They were like detectives and lawyers.". Desperation drove me to call them, and in the initial discussion, I knew I was dealing with experts who had experienced everything. Their legal experts were well-versed with international financial rules like the back of their hands. They deciphered the network of shell corporations and offshore locations quicker than I could update my email. Their technical team, no less relentless, followed the transaction trails with precision akin to a surgeon. What impressed me most was their thoroughness. Every update came with legal documentation so polished it looked fit for a courtroom. They liaised with authorities across borders, cutting through red tape with the precision of a seasoned diplomat. When obstacles arose, and they did, the team adapted without breaking stride. Their persistence became my anchor. Exactly 27 days after my initial call, I received an email that made my heart skip. My Bitcoin had been recovered and safely transferred to my new secure wallet. I stared at the screen, tears mixing with disbelief and relief. GRAYWARE TECH SERVICES not only retrieved my money but also restored my faith in getting finances. They guided me through the entire process of protecting my assets in this unstable world known as the online space. I now sleep soundly knowing that an impenetrable system shields my backside, thanks to their assistance. Their legal acumen is as sharp as their technological prowess. I owe my financial future to their tireless work. They truly are the guardians of the digital age. You can reach them on web at ( https://graywaretechservices.com/ ) also on Mail: ([email protected]) whatsapp (+18582759508)
06.04.25 02:29 famousmullica

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06.04.25 11:30 maryjul75

As at September this year I got scammed by a fake investment broker, they took my savings, happiness, health, hope, trust and left me in tears and agony. My next thought was capitalized on suicide attempts, I also tried two different hackers who lured me to borrow for my colleagues but yet another scam. I saw a link on my Facebook group which I joined and luckily I came across www.fastrecoveryagent.com, they work in hand with the FBI in the united states. So I reported my case with evidence of payment made to the so-called investment broker, the ic3 investigator's carried out investigation to confirm if I was also tell the truth and after they must have concluded on my case I received back my money. I'm so grateful for your help today, words alone can't show how Happy and Alive I'm ever since I came across your great works. Thanks once more.
07.04.25 11:16 Lindaporche5

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07.04.25 11:16 Lindaporche5

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07.04.25 18:09 rashmiramesh

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07.04.25 18:32 elizabethrush89

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07.04.25 18:32 elizabethrush89

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07.04.25 21:03 elizabethrush89

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08.04.25 03:00 natashaohnson

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10.04.25 23:26 patricialovick86

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10.04.25 23:27 patricialovick86

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11.04.25 00:48 patricialovick86

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11.04.25 03:20 edwardoelliott6

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11.04.25 08:10 Beatrice Gallagher

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13.04.25 01:13 michaeldavenport218

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13.04.25 01:13 michaeldavenport218

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14.04.25 23:44 elizabethrush89

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17.04.25 03:56 tylerkevin

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18.04.25 20:39 michaeldavenport218

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18.04.25 20:39 michaeldavenport218

I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1
19.04.25 02:00 [email protected]

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20.04.25 00:45 khouser

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20.04.25 17:22 patricialovick86

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20.04.25 17:22 patricialovick86

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21.04.25 03:51 gleerandon

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21.04.25 12:19 michaeldavenport218

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