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Sensors and Materials, Vol. 33, No. 11 (2021) 4017–4030
MYU Tokyo
S & M 2742

Elimination of Motion Artifacts
in Photoplethysmography Signals by Analytical Method
Hualong Guo,1 Yang-Han Lee,2* Yi-Lun Chen,2
Shengrong Lu,1 and Hsien-Wei Tseng1**
1College of Mathematics and Information Engineering, Longyan University, Fujian 364012, China

2Department of Electrical and Computer Engineering, Tamkang University, New Taipei City 251301, Taiwan(Received July 1, 2021; accepted November 16, 2021)

Keywords: photoplethysmography (PPG), electrocardiography (ECG), independent component analysis,
motion artifacts, multi-bandpass filter

Taiwan currently faces an aging population and a rise in mortality rate caused bycardiovascular disease. Therefore, the prevention of cardiovascular disease and the constant
tracking of physiological information are crucial. Photoplethysmography (PPG) is used to
instantaneously measure and monitor a person’s physiological information. Compared withelectrocardiography, PPG measurements are more convenient and less expensive. However, PPG
is more susceptible to the effects of motion artifacts. To accurately analyze the physiologicalinformation contained in PPG signals, the negative effects of motion artifacts on PPG signals
must first be eliminated. In this study, independent component analysis was employed toseparate independent components (i.e., PPG signals and noise) from raw signals with motion
artifacts. Subsequently, independent components containing PPG signals were selected and thelocations of the PPG signal components in the frequency spectrum were analyzed. Next, the raw
signals were passed through a multi-bandpass filter specifically designed for this study toeliminate motion artifacts. Motion artifacts were created for an experiment using two types offinger movements: vertical and horizontal finger movements. From the independent component
analysis of the independent components, the waveforms of the filtered PPG signals in the timeand frequency domains were acquired, which were then compared with the results of heartbeat
measurement.

1.

Introduction

As the standard of living rises and medical equipment and technology advance, average life
expectancy continues to improve. According to the year-end demographic structure analysis
conducted by the Department of Statistics of the Ministry of the Interior in 2013, the percentageof people over 65 years old continued to rise after Taiwan became an aging society in 1993. By
2013, that percentage had reached 11.53%, an increase of 2.29 percentage points from 9.24% at
the end of 2003. Although population aging signifies a decline in average mortality rate, heartdisease has become increasingly common; it was the fourth leading cause of death in 1996 but*Corresponding author: e-mail: yhleepp@gmail.com**Corresponding author: e-mail: hsienwei.tseng@gmail.com

https://doi.org/10.18494/SAM.2021.3525

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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the second leading cause of death in 2012 according to cause-of-death statistics provided by the
Department of Statistics of the Ministry of Health and Welfare.(1) The mortality rate has also
increased annually. At present, the instantaneous monitoring of physiological information is amajor topic of study in sports and in medical treatment.
The most well-known methods used to monitor physiological information areelectrocardiography (ECG) and photoplethysmography (PPG). PPG is based on opticalproperties, where light changes detected by optical components are used to measure thecardiovascular system and its physiological parameters. PPG features advantages such asease of use, diversity of measurement locations, and low cost; however, the disadvantage
is that signals are prone to the effects of external interferences (artifacts). To accurately
measure physiological information, the properties and composition of PPG signals must
be clearly understood. The types of signals exhibiting motion artifacts and the causes ofthe motion artifacts must be analyzed to separate or remove the interfering signals. To
address this need, in this study we proposed a method of eliminating motion artifacts.

2.

Methodology

2.1

PGG

PGG is a noninvasive method used to measure physiological signals. This method involves
the selection of a skin area, which is subsequently irradiated with red, green, or IR LED light, as
schematically shown in Fig. 1. As the light penetrates the skin, it is deflected because of changes
in the vascular caliber. Because parts of the light source are also absorbed by the blood, the lightsource undergoes continuous changes. Images constructed using the changing light are called
PPG images. PPG signals contain information such as heart rate, respiratory rate, oxygen
saturation, pulse reflection index, and pulse wave velocity.
2.1.1 Properties of PPG signals in time and frequency domains
The time domain analysis of PPG signals is commonly used to detect heartbeat frequency. As
shown in Fig. 2, the distance between two wave crests is the time between heartbeats (the cardiac

Fig. 1.

(Color online) Schematic diagram of PPG signals measured by reflection measurement.(2)Sensors and Materials, Vol. 33, No. 11 (2021)

Fig. 2.

Fig. 3.

4019(Color online) Schematic diagram of continuous PPG waveform.

(Color online) PPG signal distribution plotted as frequency spectrum.(3)cycle). By counting the number of such distances in 1 min, the heart rate [beats per min (bpm)] is
obtained.
By converting PPG signals to a frequency spectrum using the Fourier transform, physiologicalinformation such as the heart and respiratory rates can be obtained. Figure 3 shows a converted
frequency spectrum featuring “clean” PPG signals (without motion artifacts); in the frequency
domain, PPG signals consist of a fundamental wave, a second-harmonic wave, and a thirdharmonic wave. The fundamental wave frequency can also be used to indicate the frequency ofheartbeats per second. In Fig. 3, the fundamental wave crest exhibits a frequency ofapproximately 1.6 Hz. By multiplying the frequency by 60, an average heartbeat of approximately
96 bpm can be calculated.
2.2

Motion artifacts

When measuring PPG signals, physiological signals are prone to interference (motion
artifacts) from external factors. The origins of motion artifacts vary, but can primarily be
divided into poor contact with sensing elements, interference from surrounding lights, andinterference from measuring instruments caused by participant movement (shaking) during
measurements,(4) the last of which is the most significant.

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3.

Methods of Eliminating Motion Artifacts

3.1

Independent component analysis

Independent component analysis (ICA) is a statistical, computational, and linear
transformation method.(5–10) ICA can be used to separate observed mixed signals into
independent, non-Gaussian distributed signals. The independent signals are occasionally called
the independent components of the mixed signals.
Figure 4 shows a schematic diagram of the cocktail party problem. Four people are assumed
to be talking to each other simultaneously in a quiet environment, and each of them is assumed
to be able to identify the sound of the listener. Concurrently, four microphones are placed in theroom at various locations to collect the sounds. The mixed sounds collected by the microphones
can be represented by the following mathematical equations.
x1 (t ) = a11s1 (t ) + a12 s2 (t ) + a13 s3 (t ) + a14 s4 (t )x2 (t ) = a21s1 (t ) + a22 s2 (t ) + a23 s3 (t ) + a24 s4 (t )x3 (t ) = a31s1 (t ) + a32 s2 (t ) + a33 s3 (t ) + a34 s4 (t )(1)x4 (t ) = a41s1 (t ) + a42 s2 (t ) + a43 s3 (t ) + a44 s4 (t )Here, a11, a22, ..., a44 are the weighted parameters of the distance between the microphones andthe sources of the sounds.
3.1.1 Basic definition of ICA
In general, signals collected during signal collection are mixed signals, where the patterns of
the mixed and raw signals are unknown. The raw signal is typically difficult to identify.
However, ICA is able to separate the raw signal s(t) from the mixed signal x(t) when x(t) is
known. The basic model equation for ICA is as follows:

Fig. 4.

(Color online) Schematic diagram of cocktail party problem.

Sensors and Materials, Vol. 33, No. 11 (2021)

 x1 
x 
 2
x3 
x(t ) =
=
 
  
 xm  a11 a12a
 21 a22
 a31 a32


 
a
 m1 am 2

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a13 … a1n   s1 
a23 … a2 n   s2  
s3  As (t ) ,a33 … a3n  =      
am3 … amn   sn (2)where A is an m × n mixing matrix that represents the weighted parameters between theobserved mixed signal x(t) and the original independent signal s(t).
3.1.2 Actual and simulation examples
As reported in this section, actual examples of mixed signals and those created fromsimulations were used, and changes in mixed signals were calculated by ICA. Results of thesimulated mixed signals are shown in Fig. 5.
Figures 5(a1)–(a3) show the original independent signals, which comprised sine, square, andtriangle waves, respectively. Figures 5(b1)–(b3) show the mixed signals, which consist of
mixtures of sine and square waves, square and triangle waves, and sine and triangle waves,respectively. Figures 5(c1)–(c3) show the results after ICA was used; the output signals reveal thecharacteristics of the sine, square, and triangle waves, respectively.
Following the above simulation, actual PPG signals were analyzed. As shown in Fig. 6, these
PPG signals were mixed with motion artifacts (created by vertical finger movements), which aresuperimposed on the frequency spectrum. The components with different frequencies were thenseparated by ICA.

Fig. 5.

(Color online) ICA simulation results.

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Fig. 6.

3.2(Color online) Results of ICA performed on actual PPG signals.

Correlation coefficient

The correlation coefficient is a statistical indicator designed by Karl Pearson used to reflect
the correlation between variables. From a statistical perspective, the correlation coefficientmeasures the “distance from independence” between two variables. The correlation coefficientis calculated using the product–moment method, where the two variables and their mean
deviation are used as the basis of calculation. The correlation between the two variables isobtained by multiplying the two mean deviations. For example, the correlation coefficient (ρX,Y)of variables X and Y is

ρ X ,Y =cov ( X , Y )σ X σY,(3)

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where cov(X, Y) is the covariance of X and Y, and σX and σY are the standard deviations of X andY, respectively.
In the methods employed in this study, correlation coefficients were used to select theindependent components. The correlation between the analyzed independent components andthe PPG signals without motion artifacts was studied using the frequency spectrum. The
independent component with the greatest correlation coefficient was chosen as the primary
component. Figure 7 shows the correlation coefficients between PPG signals without motion
artifacts and independent components 1, 2, and 3, which were 0.1549, 0.1519, and 0.5278,
respectively. Because independent component 3 featured the highest correlation, it was selected
for subsequent analysis.
3.3

Spectrum analysis

Information concerning the analysis of PPG signals on the frequency spectrum was described
previously. The PPG signals on the frequency spectrum are composed of fundamental andharmonic waves. To obtain clean PPG signals, the frequency and location of the fundamental
and harmonic waves must first be identified. However, signals contaminated by motion artifacts
cause misjudgment of the frequency and location of the fundamental and harmonic waves.
Therefore, in the two previous sections, the correlation coefficients between the PPG signals andthe independent components were analyzed and compared by ICA and the frequency domain
method, after which the desired independent components were effectively separated. As reported
in this section, a simple method was designed to determine the peak frequencies of thefundamental and harmonic waves.

Fig. 7.

(Color online) Comparison between correlation coefficients of three independent components.

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The procedure of this method is shown in Fig. 8. First, the maximum value in the 0.5–5 Hz
frequency band was identified. Subsequently, the peak frequency f1 of the fundamental wave
was obtained. Next, using the characteristics of the harmonic waves, the frequency region of f1
was expanded by a factor of 2–3 to attain the maximum value in this region. The detection
ranges were 2f1 ± 0.3 Hz and 3f1 ± 0.3 Hz. The detected peak frequencies are shown in Fig. 9.

Fig. 8. (Color online) Procedure for detecting peak frequencies of fundamental wave and second and third
harmonic waves.

Fig. 9.

(Color online) Schematic diagram of detected peak frequencies.

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After acquiring the peak frequencies of the fundamental wave and the second- and thirdharmonic waves, the components of these three waves were extracted using a multi-bandpass
filter, which was designed to extract the fundamental and harmonic waves from the original
PPG signals.
3.4

Heart rate detection algorithm

When reading PPG signals, the current heart rate can be determined by calculating the timedifference between two wave crests. Therefore, to obtain accurate heart rate information, theprecise detection of the locations of the wave crests is required. The crest detection algorithm
developed in this study was based on the bigger fall side method proposed by Navakatikyan etal. in 2002(11,12) and the improved methods proposed by Chen in 2004.(13) The idea was inspiredby the fact that wave crests and troughs have the widest gap in a waveform. By observing
complete PPG waveforms, no turning points were found between the wave troughs and theadjacent crests, and the vertical distance between the two extrema was the greatest. Therefore,
by detecting all of the extrema in a PPG waveform, calculating the differences between theextrema, and setting a determination condition to detect the locations where the greatest
difference occurred, the locations of the wave crests and troughs can be identified.

4.

Experimental Results

4.1

Experimental equipment and procedure

In this study, a reflective PPG measurement method was adopted. In the experiment,
measurements were performed at the tip of an index finger, as shown in Fig. 10. A green LED
emission light was used for analysis. Three light sensors were installed on the device for light
reception. The three light sensors simultaneously collected the green LED light that wasreflected after transmitting through the finger, which produced three original data points foranalysis. The sampling frequency of the measuring device was set at 100 Hz, and theexperimental platform MATLAB was used for simulation analysis.

Fig. 10. (Color online) Schematic diagram of PPG measuring device.

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In the experiment, two types of continuous motion artifacts were produced using vertical andhorizontal finger movements. Two experiments were performed for each type of movement.
4.2

Experimental scenarios and results of analysis

4.2.1 Vertical finger movement
The three original PPG signals are shown in Fig. 11. The left side of the diagram shows the
waveform observed in the time domain and the right side shows the corresponding frequency
spectrum.
The original PPG waveform diagram shows the significant effect of motion artifacts on the
PPG waveform. Because the corresponding frequency of the heart rate component “peakfrequency of the fundamental wave” could not be identified on the frequency spectrum, ICA
was employed to separate the independent components from the raw signals (Fig. 12).

Fig. 11. (Color online) Raw measurement signal (vertical finger movement).

Fig. 12. (Color online) Three independent components obtained by ICA (vertical finger movement).

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Once the frequency composition of the PPG signals was identified, a multi-bandpass filterfeaturing the same frequency was designed. Subsequently, original data were inserted into thefilter to eliminate motion artifacts, as shown in Fig. 13.
The algorithm described in Sect. 3.4 was used to compute the processed PPG signals to
calculate heart rate information, as shown in Fig. 14.
4.2.2 Horizontal finger movement
An experiment was performed to analyze the measurement of horizontal finger movement,
which was carried out by the same process as that used for the vertical finger movement. Oncethe frequency composition of the PPG signals was identified, a multi-bandpass filter featuring
the same frequency was designed. Subsequently, the original data were inserted into the filter toeliminate motion artifacts, as shown in Fig. 15.
The algorithm described in Sect. 3.4 was used to compute the processed PPG signals to
calculate heart rate information, as shown in Fig. 16.

Fig. 13. (Color online) Original PPG signals and PPG signals after processing (vertical finger movement).

Fig. 14. (Color online) Heart rate detection results (vertical finger movement).

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Fig. 15. (Color online) Original PPG signals and PPG signals after processing (horizontal finger movement).

Fig. 16. (Color online) Heart rate detection results (horizontal finger movement).

4.3

Experimental data results

The average heart rates measured by ECG were set as the reference. Next, the average heart
rates obtained from the experimental analysis of the PPG signal were compared with thereference, as shown in Table 1. The experimental results indicated that the proposed method ofanalysis can effectively eliminate the motion artifacts of PPG signals and produce favorable
waveforms. Therefore, when waveform information is complete, heart rate detection is very
precise. The integrated data in Table 1 show that the differences between the average heart rates

Table 1Comparison between average heart rates measured by ECG and those obtained by experimental analysis of PPG
signals.
Average heart rate
Average heart rate
Difference in average
Percentage(bpm) measured by(bpm) measured byheart rate (bpm)
difference (%)
ECG
PPG
between ECG and PPG
Vertical finger
E1
82.3
81.5
−0.8
0.97
movement
E2
82.8
82
−0.5
0.6
Horizontal finger E 1
88.3
89.7
+1.4
1.59
movement
E2
91.6
92.1
+0.5
0.55

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obtained from PPG and ECG waveforms ranged between 0.55 and 1.59%, indicating that theheart rates obtained from the PPG waveforms were almost identical to those obtained from the
ECG waveforms. Concerning other factors that affect physiological information, such as thevarying time of signal transfer and body movements, we concluded that the error rates of theaverage heart rate between PPG and ECG were all within a reasonable range.

5.

Conclusion and Future Prospects

PPG is used in a wide range of applications. In general, when using this method to analyze
physiological information, the patient’s body must remain stationary. When movements occur
during PPG measurement, PPG is prone to interference. Furthermore, the resulting waveforms
are affected, making analysis difficult. For example, interference with waveforms causes aninaccurate detection of the heart rate, the most crucial physiological information. In certain
scenarios, analysis is severely affected, rendering waveform analysis impossible. Therefore, amethod of eliminating motion artifacts was proposed in this study. A simulation-based
experiment demonstrated the validity of the proposed method. From the experimental results,
the average heart rate difference between PPG and ECG ranged from 0.55 to 1.59%. This
demonstrates that the information of PPG interference obtained via the proposed analyticalmethod can be effectively filtered out of the interference.
The simulation in this study was performed using MATLAB on a computer; in futurestudies, instant, real-time processing should be implemented practically in the field of medical
treatment and fitness equipment such as treadmills. However, in the real-time analysis, there aremany factors that need to be re-examined and designed; thus, there is a wide scope for further
development of the proposed method.

Acknowledgments
The works are supported by the Great project of production, teaching, research of Fujian
provincial science and Technology Department (2019H6023), supported by Longyan Scienceand Technology Project (2019LYF12010), Longyan University’s Qi Mai Science and Technology
Innovation Fund Project of Liancheng ([2018]132), and Shanghang (2019SHQM05) County,
Longyan and Longyan University’s Research and Development Team Fund ((2018)8), and theMinistry of Science and Technology, Taiwan, project of MOST 110-2221-E-032 -018 -MY2 andthe Ministry of Education, Taiwan, project of “Agriculture Artificial Intelligence Internet ofThings (AgAIoT)”.

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