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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>I. Berezhnyi);</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Multiresolution analysis of poor remote photoplethysmography signal using wavelet transform⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ihor Berezhnyi</string-name>
          <email>ihor.v.berezhnyi@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Adrian Nakonechnyi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lviv Polytechnic National University</institution>
          ,
          <addr-line>12, Bandera Str, Lviv, 79013</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>1873</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>Remote photoplethysmogram signal processing algorithms have demonstrated effectiveness as a noninvasive means of gathering data on the human cardiovascular system for rapid clinical parameter assessment. The primary objective is to extract valuable information from remote photoplethysmogram signals captured by common front cameras on smartphones or laptop webcams for subsequent analysis of the human cardiovascular system. The developed approach to processing a remote photoplethysmogram obtained from a low-quality video signal using a discrete wavelet transform and deconstructionreconstruction allows filtering and qualitatively evaluating the received signal to predict possible diseases of the human cardiovascular system. The selection of optimal mother wavelet functions provides high performance and scalability of the system in the time-frequency domain. According to the developed approaches of multiresolution analysis, the reliability of the obtained data is more than 93% and makes it possible to conduct time-resolved analysis of a low-quality video signal and identify key points of the human cardiovascular system.</p>
      </abstract>
      <kwd-group>
        <kwd>Photoplethysmography</kwd>
        <kwd>heart rate</kwd>
        <kwd>variability</kwd>
        <kwd>filtering</kwd>
        <kwd>wavelet transform1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <sec id="sec-1-1">
        <title>1.1. Remote photoplethysmography</title>
        <p>Remote photoplethysmography (RPPG) has transformed the field of physiological monitoring by
providing a non–invasive way to assess vital signs using camera–equipped devices from a distance.
As telemedicine and remote healthcare continue to grow, RPPG signal analysis is essential to provide
accurate and reliable health assessments across traditional clinical settings.</p>
        <p>
          RPPG is a non–invasive optical method that is widely used in a variety of medical and
physiological studies. Its importance stems from several key factors that make it significant in clinical
and research settings, such as non–invasiveness, versatility, accessibility, and cost–effectiveness [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ].
Non–invasiveness and convenience RPPG is performed using a non–invasive sensor. This makes it
a comfortable method for patients, allowing for regular or continuous monitoring. RPPG provides
vital information about the human cardiovascular (CV) system. It measures changes in blood volume
in the microvascular flow of tissues, which are indicative of the pulsatile information component of
the cardiac cycle. RPPG waveforms are used to calculate arterial blood oxygen saturation and
determine heart rate in pulse oximeters, which are widely used in routine clinical practice [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ].
        </p>
        <p>
          This capability makes RPPG useful for monitoring heart rate, blood oxygen saturation (SpO2),
and other hemodynamic parameters. In clinical settings, RPPG is used for anesthesia monitoring,
sleep studies, and autonomic function assessment. RPPG devices are relatively inexpensive and
simple compared to other cardiovascular monitoring technologies such as electrocardiography
(ECG) or echocardiography (EEG) [
          <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
          ]. This affordability makes RPPG accessible in both high and
low resource settings.
        </p>
      </sec>
      <sec id="sec-1-2">
        <title>1.2. Problem statement</title>
        <p>
          Today, there are a variety of methods for extracting the RPPG signal from the camera video stream,
as well as filtering algorithms [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ], but most of them are designed for systems with a large number of
frames, most often 60fps (frames per second), and high FHD resolution. Such algorithms are
inefficient and unworkable with the front–facing cameras of common smartphones, laptops, and
notebooks, which have frame rates of 15fps to 30fps at low SD and HD resolutions. One of the key
problems is the loss of information in the RGB signal and image distortion due to low resolution and
high noise levels (lighting changes, motion in the frame, etc.) in the video stream [
          <xref ref-type="bibr" rid="ref1 ref5">1, 5</xref>
          ]. This leads to
difficulties in analyzing the necessary critical points of the human cardiovascular system (CVS) for
the analysis of RPPG signals, such as:
•
•
•
•
        </p>
        <p>
          Reduced accuracy of face and key point extraction: Poor video quality makes it difficult to
accurately extract the face area and identify key points [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ]. This adversely affects the
subsequent analysis of the RGB signal and facial skin color fluctuations required for RPPG
signal extraction.
        </p>
        <p>
          Noise and artifacts present in low–quality video can mask real skin color changes caused by
blood pulsation [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ].
        </p>
        <p>
          Low image resolution leads to reduced spatial clarity and unwanted artifacts, which makes it
difficult to analyze changes in RGB space [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ].
        </p>
        <p>
          Variable lighting makes it difficult to normalize colors and further complicates the extraction
of skin–color–dependent signals. In conditions of low video quality, this effect becomes even
more pronounced and significantly distorts the received RPPG signal [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ].
        </p>
      </sec>
      <sec id="sec-1-3">
        <title>1.3. The purpose of the study</title>
        <p>The aim and objective of the study is to develop an algorithm and principles for processing RPPG
signals received from laptop webcams or smartphone front cameras with low fps (15–20fps) by using
wavelet transform and wavelet filtering of the received signals, as well as the deconstruction–
reconstruction method. Analysis of received wavelet coefficients and separation of specific
coefficients that contain information about the human nervous system. This involves the
development of an algorithm for multi–resolution filtering of the input signal (RPPG) and
identification of key points necessary for the analysis of the human cardiovascular system. Selection
of mother wavelet functions for filtering RPPG signals by comparing the obtained results with
medical devices. Analysis of the received wavelet coefficients in the time-frequency domain. Forming
a scalogram to compare the RPPG signal before and after filtering.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Materials and Methods</title>
      <sec id="sec-2-1">
        <title>2.1. Ethics and Dataset</title>
        <p>
          The study was conducted on the UBFC–rPPG [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ], PURE [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ], SCAMPS [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ], UBFC–Phys [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] datasets,
as well as internal recordings using a Google Pixel 4 mobile phone. The studied datasets contain
more than 120 videos with 62 subjects. These videos contain different characteristics of cameras,
lighting, room, resolution, and number of frames per second. In total, videos with Standard Definition
(SD), High Definition (HD), and Full High Definition (Full HD) resolutions were analyzed. The videos
have a different number of frames per second, namely: 10fps, 15fps, 20fps, 30fps, and 60fps.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Wavelet transform method</title>
        <p>Wavelet filtering is known to be a powerful signal processing tool that is widely used to analyze
remote photoplethysmography (RPPG) signals. Such filtering has clear advantages and
disadvantages when applied in this field. One of the most important advantages is the ability to
effectively suppress noise and artifacts while preserving signal features on different time scales. The
decomposition of RPPG signals into wavelet coefficients with different resolutions allows for
selective noise removal, improving the signal–to–noise ratio and the accuracy of parameter
estimation and signal interpretation.</p>
        <p>Wavelet filtering is a versatile yet adaptive method for removing signal noise in RPPG analysis,
allowing researchers to customize the filtering process to suit unique signal characteristics and noise
sources. Wavelet filters can be tuned to specific frequency bands or spatial regions in the signal,
resulting in precise noise suppression while minimizing distortion of the underlying physiological
information. Wavelet filtering is a powerful tool for detecting and removing transient or non–
stationary noise components in RPPG recordings that are affected by motion artifacts or
environmental perturbations.</p>
        <p>It is important to note that, like any method, it has its limitations. The complexity associated with
choosing the basis functions and designing filters, especially when the signal has multiple
overlapping components or nonlinearities. To achieve the best noise reduction performance and
avoid artifacts or signal distortion, it is important to choose the appropriate type of basis wavelet,
number of decomposition levels, and thresholding method. Wavelet filtering can introduce edge
effects or artifacts at the signal boundaries, potentially affecting the accuracy and reliability of the
results.</p>
        <p>
          Wavelet filtering can be problematic in real–time or near–real–time applications, especially when
working with large datasets or high–resolution signals. However, with proper optimization, wavelet
decomposition and reconstruction can be made scalable and applicable in resource–constrained
environments or in embedded systems [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]. While wavelet filtering offers significant advantages in
noise suppression and signal reduction in RPPG analysis, it can be difficult for non–specialists to
interpret due to the complexity of performing wavelet transforms and using appropriate
thresholding methods. However, it should be noted that these limitations can be overcome with
proper optimization. In general, wavelet filtering is an important and powerful tool for analyzing
RPPGs, provided that the appropriate transformation characteristics are skillfully and correctly
selected.
        </p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Wavelet deconstruction</title>
        <p>The discrete wavelet transform (DWT) of RPPG signals provides time–referenced frequency
information that allows us to operate on the signal and analyze its critical changes and positions in
time–frequency space using the RPPG signal decomposition levels (Figure 1).</p>
        <p>Figure 1 shows the plethysmogram (PPG) signal, specifically, an example of a PPG signal from a
medical device obtained by RPPG from video images. The RPPG signal is presented after level 3
wavelet deconstruction–reconstruction and the RPPG signal after wavelet thresholding and
decomposition coefficient filtering using a Bandpass filter with a setting of 0.7Hz. During wavelet
transform or wavelet deconstruction, the resulting coefficients (Figure 2) can be interpreted as a
separate component of the input signal. Such components describe the informative part of the RPPG
input signal at selected frequencies, which allows the signal to be evaluated in time–frequency space.
It is worth noting that the number of coefficients decreases with increasing reconstruction level, so
changes from filtering bring significant changes to the original signal.</p>
        <p>
          After reconstructing the PPG signal received from the Google Pixel smartphone and the front
camera resolution of 640×480px (0.3 MP) with a frame rate of 20 frames per second, the resulting
RPPG signal can be represented as a set of wavelet coefficients (Figure 2). After analyzing the video
from the UBFC–rPPG [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ], PURE [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ], SCAMPS [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ], UBFC–Phys [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] datasets, it was concluded that,
depending on the resolution and the number of frames per second, it is necessary to perform wavelet
decomposition up to seven levels. The decomposition of the eighth and higher levels does not contain
an information component for analyzing RPPG signals obtained from a low–quality camera.
        </p>
        <p>The obtained decomposition coefficients can be represented as signal graphs (Figure 3), where
each level corresponds to the level of decomposition of the RPPG signal. Accordingly, the zero level
is the representation of the input RPPG signal, the first level of the decomposition is the composition
of the signal without one coefficient in the wavelet decomposition of the signal.</p>
      </sec>
      <sec id="sec-2-4">
        <title>2.4. Wavelet deconstruction</title>
        <p>To determine the parameters of the PPG signal, namely, the systolic and diastolic peak, and
variability, the obtained RPPG signal was analyzed with a level 3 wavelet decomposition. The
classification of these parameters is conducted by finding the maxima and minima of the signal,
taking into account their amplitude (Figure 4). A part of this signal is shown in Figure 5.</p>
      </sec>
      <sec id="sec-2-5">
        <title>2.5. Information component of the cardiovascular system</title>
        <p>The influence of wavelet decomposition levels on the content of the information component on
cardiovascular activity is investigated. The direct dependence of some levels of the decomposition
on the parameters of the cardiovascular system was found. Figure 6 shows the signal of the 3rd level
of reconstruction, which corresponds to the heart rate, as well as the variability of the cardiovascular
system (IBI). Figure 6 shows a comparison of the IBI signal obtained from the RPPG and the signal
from the medical device. The RPPG signal contains interference such as missing frames, motion in
the frame, and changes in lighting, which is tracked in the peaks that are present in the RR signal.</p>
        <p>This study was carried out on the specified datasets, the results of which are shown in Table 1.
However, if the interference data is filtered out using a simple Bandpass filter with a level of 0.7Hz,
the resulting signal will correspond to the medical signal by 85–94% (corresponding to the number
of frames per second). The median of this signal will be 0.85ms, and considering the double standard
deviation, to determine the permissible deviation, it will be from 0.35ms to 1.35ms. Figure 6 also
shows the relationship between heart rate and the variability of the human cardiovascular system,
with an average heart rate of about 55–63 beats per minute.</p>
        <p>MEAN is the root-mean-square value of the signal.</p>
        <p>MEDIAN is the average value of all data ordered from smallest to largest.</p>
        <p>RMSSD is the root-mean-square of successive differences in signal values.</p>
        <p>SD – standard deviation, or a statistical measure of variability that indicates the average
amount of deviation of a set of numbers from their mean value.</p>
        <p>Error – the percentage of values with an error relative to the medical equipment.
Confidence – the value of the correspondence between the signal from the medical device
and the signal obtained as a result of wavelet transformation.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Architecture diagram</title>
      <p>
        RPPG algorithms typically use face recognition techniques to identify regions of interest (ROIs) in
the resulting images [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. The architecture in Figure 7 describes further processing, which involves
selective filtering of skin pixels based on empirically derived color thresholds, which helps to extract
signals that indicate the dynamics of blood perfusion.
      </p>
      <p>
        Modern signal processing methods, such as clustering and Bandpass Filtering algorithms,
effectively reduce the impact of negative factors such as motion artifacts and environmental noise.
These algorithmic approaches facilitate non–invasive and continuous monitoring of cardiovascular
parameters, which has promising implications for various fields, including healthcare, health
monitoring, and human–computer interaction research [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>The proposed architecture solves a number of problems of the remote photoplethysmography
approach using the following elements:
•
•
•
•
•</p>
      <p>Video conversion and frame–by–frame reading element (this element allows processing both
recorded video and video stream, regardless of whether it is a physical camera or a stream
from the cloud).</p>
      <p>Face and landmark detection (the element of detecting faces in the frame, recognizing faces
and landmark control points).</p>
      <p>RGB signal analysis.</p>
      <p>Input signal evaluation (provides control over the incoming video).</p>
      <p>Wavelet transform and filtering (provides time–frequency analysis of the signal with
subsequent filtering).</p>
      <p>
        The basic principle of multi–resolution analysis of the RPPG signal is shown in Figure 8. Different
sets of mother wavelet functions were used for the study, and as a result, the dmay mother function
was chosen [
        <xref ref-type="bibr" rid="ref10 ref11">10, 11</xref>
        ].
      </p>
      <p>The first phase is the decomposition of the input RPPG signal into coefficients, this process is
called signal deconstruction. Each pair of Low Pass (LP) and High Pass (HP) coefficients corresponds
to a certain frequency range of the input signal. Having received a set of coefficients after wavelet
deconstruction of the signal, frequencies with noise, such as coefficients of the 1st level of
decomposition, namely in the range of 500kHz – 250kHz, are discarded. The 0Hz – 36Hz frequency
and the high frequencies of 250Hz – 500Hz, where noise artifacts are present, are best filtered using
wavelet filtering.</p>
      <p>
        The wavelet transformation is performed using the dmey of the parent wavelet function [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. The
coefficients of the second level of decomposition should be filtered using a Bandpass filter with a
setting of 0.7Hz, this will allow filtering out the interference that is present in the main signal, such
as: movement in the frame, sudden changes in lighting, camera artifacts and input image artifacts.
Together with the following coefficients, a set is formed that is used in the second phase. The second
phase consists in reconstructing the signal using the previously calculated coefficients. The output
of this scheme is the RPPG–filtered signal for further analysis and determination of cardiovascular
characteristics.
      </p>
      <p>The paper discusses the main elements of the remote photoplethysmography algorithm to
evaluate their performance and the noise that can be generated during RGB signal compression or
analysis. Noise, in turn, degrades the quality of the signal under study.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Experiments and results: multiresolution analysis of RPPG signal</title>
      <p>Multi–resolution analysis of the signal after wavelet filtering and decomposition aims to display the
spectrogram (Figure 9) of such a signal for the purpose of visual representation and further analysis
of the RPPG signal.</p>
      <p>The basis of multi–resolution analysis is the result of the DWT transformation, which can be
displayed using a spectrogram. Figure 10 shows the signal before filtering is applied, and Figure 11
shows the signal with wavelet filtering, using wavelet analysis and playback.</p>
      <p>
        Such a representation allows evaluating the informative component of the signal and compare it
with the original. The spectrogram obtained using CWT of the filtered signal is shown in Figure 12.
This graph shows the signal in the time–frequency space, where there are pronounced planes with
peaks that correspond to the peaks and low levels of the RPPG signal. It is worth noting that it is
difficult to separate implicit signal changes, such as the dicrotic component, in such a spectrogram.
Figure 13 shows the O and S components [
        <xref ref-type="bibr" rid="ref12 ref13">12, 13</xref>
        ] superimposed on the CWT spectrogram. The main
informative part is present in the range of 100–300Hz. The signal containing interference and errors
is located in the range of 350–500Hz and above.
      </p>
      <p>Figure 10 shows the scalogram of the signal before filtering, on which there are noises
corresponding to frequencies of 90Hz - 250Hz. Also, the main RPPG signal, which is necessary for
SS, is not localized, as evidenced by the large area of the signal at the frequency of 40Hz - 80Hz.
Comparing the scalograms of the signals in Figure 10 and Figure 11, it can be stated that after the
application of multisection filtering, the RPPG signal has a smaller signal area, and there is no noise
at higher frequencies. This can also be observed in Figure 12, where the RPPG signal is displayed,
namely the peaks that are necessary for CVS analysis. The correspondence of the peaks between the
scalogram and the determined maxima and minima of the RPPG signal is shown in Figure 13, where
you can visually confirm the correct application of the filter.</p>
      <p>Multi–resolution analysis can be presented in the form of a graph on which informative
frequencies are separated with a certain step (Figure 14). Such a graph will show the signal
components after wavelet transformation, considering the step between each signal, which allows
evaluating the dependencies between different signal frequencies and separate the high and low
frequencies. The signal at high frequencies is visually distinguished from the signal at low
frequencies by the presence of interference. Also, we can visually observe the movement of the
subject in the frame between 40 and 50 seconds (Figure 15 and Figure 16).</p>
      <p>The results of the multiresolution analysis indicate that it is possible to obtain a clear display of
the heart rate component on the RPPG signal (Figure 17). With the selected components (systolic
and diastolic peaks), it is possible to analyze diseases of the human cardiovascular system. Also, these
results can be interpreted as CVS variability.</p>
      <p>
        Filters perform a key role in the analysis of RPPG signals by helping to reduce noise and hence
improve feature extraction and parameter estimation. This evaluation aims to thoroughly examine
the various filters commonly used in RPPG analysis, identify their main steps, and evaluate their
effectiveness in addressing the key requirements [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] inherent in the analysis process [
        <xref ref-type="bibr" rid="ref14 ref15">14, 15</xref>
        ] and
compare them to the new multiresolution approach.
      </p>
      <p>The results of the multiresolution analysis in comparison with the known approaches are
presented in Table 2 and Table 3. Videos with a frame rate of 30fps or more were excluded from the
analysis because the focus of the study is on signals obtained from low–quality videos. The analysis,
which is commonly used for RPPG, showed that the root–mean–square error for several types of
filters indicates the effectiveness of these filters for noise reduction, feature extraction, and
parameter estimation (RMSE is about 1 bit/s).</p>
      <p>
        The low RMSE values (Multiresolution wavelet analysis, Savitzky–Golay [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ], Deep Learning
[
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]) for different filters indicate accurate signal processing, demonstrating their potential to
improve the accuracy and reliability of RPPG analysis in various applications. The comprehensive
RMSE evaluation provides valuable information about the performance of each filter. Overall, the
RMSE analysis emphasizes the importance of robust signal processing techniques in RPPG analysis.
      </p>
    </sec>
    <sec id="sec-5">
      <title>5. Discussion</title>
      <p>The research project is expected to provide a system for analyzing the RPPG signal from a
lowquality video stream. In order to separate the components of SS, and to design a system of diagnosis
of CVS and detection of diseases. Wavelet filtering offers a versatile approach to noise suppression
and feature extraction, effectively removing noise and preserving signal features at different time
scales. Such adaptability is particularly useful in RPPG analysis, where signals may have dynamic
and non-stationary characteristics due to physiological variations, or directly from a low-quality
signal that contains many interferences caused by artifacts present in the video.</p>
      <p>
        At the preliminary stages, we define specific areas and tasks, anticipating future requirements for
the designed multipart RPPG signal analysis systems. The correct use and selection of basic mother
functions ensures the accuracy of PPG signal reproduction [
        <xref ref-type="bibr" rid="ref10 ref11">10, 11</xref>
        ].
      </p>
      <p>Multiresolution approach has been developed for the analysis of the RPPG signal obtained from
a video camera of low quality and low frame rate. The approach provides a qualitative analysis of
the basic components (systolic and diastolic peak, dicrotic component, heart rate, variability) of the
cardiovascular system, with an accuracy of 84% to 95%. This allows the use of household cameras
(mobile phones) to monitor and analyze the human cardiovascular system remotely, without using
additional devices and, most importantly, to ensure non-invasiveness.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusions and Future work</title>
      <p>In conclusion, multiresolution approach for the analysis of the RPPG signal using multipartition
CWT analysis has been developed. Which allows evaluating the variability and frequency of the
heartbeat using a spectrogram. Using the datasets, the main informative section of 100-300Hz was
formed for the analysis of the cardiovascular system. Defined algorithms for wavelet
analysisreproduction by wavelet transformation levels. The main information levels are highlighted, such as:
levels 3 and 4 for determining R and O peaks, levels 5-6 allow for the assessment of respiratory
fluctuations, levels 1-2 contain interference depending on the lack of lighting, movement in the frame
or lack of frames for the assessment of the RPPG signal. Thus, the wavelet filter is an effective
solution for analyzing remote photoplethysmography signals due to its versatility, reliability, and
interpretability. By effectively suppressing noise and preserving signal features, the wavelet filter
improves the accuracy and reliability of RPPG analysis, offering valuable information for clinical
diagnosis, physiological monitoring, and scientific research. This filter reliably delivers accuracy as
shown by the results from the RMSE comparison of 1.19 beats per minute. Future advances in wavelet
signal processing technologies promise to further improve the efficiency and applicability of RPPG
analysis in various conditions.</p>
      <p>Prospects for further research by the authors are to further study photoplethysmographic signals,
to analyze in detail the extended components of the RPPG signal to provide a reliable and accurate
method for diagnosing the human cardiovascular system using signals from low–quality video
cameras.</p>
    </sec>
    <sec id="sec-7">
      <title>Acknowledgements</title>
      <p>I gratefully acknowledge the support and expertise of researchers at Lviv Polytechnic National
University. Their valuable insights and assistance were instrumental in the development and
completion of this research.</p>
    </sec>
    <sec id="sec-8">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the authors used DeepL and Grammarly in order to: Grammar
and spelling check, paraphrase, reword, identify and correct grammatical errors. After using these
tools, the authors reviewed and edited the content as needed and takes full responsibility for the
publication’s content.</p>
    </sec>
  </body>
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