# One Method for Preprocessing Pulse Signal Based on Deep Learning

Authors: Zhao Liguo; Li Zhixian
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The collection of pulse signals is accompanied by considerable noise interference, and it is necessary to denoise the collected signals to eliminate the error brought about by the outside world and the instrument itself to the actual data to the greatest extent. Considering this, this article proposes a preprocessing scheme for noise reduction. Firstly, the saturation detection algorithm in signals is based on the gradient, and extreme is utilized to remove the saturation interference. On this basis, the artifact detection module based on complex network connectivity is proposed. Finally, the self-adjusting parameter integer coefficient filtering is utilized to include the baseline drift. The noise inside is filtered out. The experimental results demonstrate that the proposed method, in the case of a similar signal-to-noise ratio, has a mean square error of 15.7 and a shorter convergence time of 0.02s.


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## Body

## 1. Introduce

Most of the existing pulse signal preprocessing methods use the filter to remove the noise [1–6] and baseline drift [1, 2, 7, 8] coupled into the pulse signal. Regardless of noise or baseline drift, for pure signals, it is generalized noise. There are essentially three types of filtering noise: the first one is the digital filter IIR, the second type is the empirical mode decomposition EMD, and the third type is the wavelet transform. However, the pulse signal is subject to more types of interference during the acquisition process, and some of the interference are more serious and cannot be enhanced by the existing preprocessing method. The former has lost information at the time of acquisition. The latter frequency band and pulse signal mutual signal saturation and artifacts are two mutual interference overlaps that are arduous to remove. The removal of these two kinds of interference is relatively hard. The detection of such difficult-to-remove distortion is extremely important for the analysis of pulse signals, especially in the real-time monitoring of pulse signals. In these problems requiring long-term detection of pulse signals, it is therefore difficult to manually mark the location of the pulse signal that contains these disturbances.Considering this, after analyzing the two kinds of interference signals and their causes, the corresponding detection algorithms are given. For the detection of saturated signals, this section proposes the quasi-side of the saturation signal detection according to the definition of saturation. For the detection of artifacts, the current existing method is built on the extraction of statistical information from the pulse signal. After extracting the statistical information such as the mean value, variance, and sample entropy from the pulse signal, a threshold is set on the statistical information to detect a signal containing artifacts [9,10]. Since the empirical mode decomposition (EMD) method can separate the high-frequency part of the signal, and the frequency of artifacts tends to be high, empirical mode decomposition is also often used for artifact detection [11–13]. These methods can only detect whether there are artifacts in the pulse signal. However, it is sometimes difficult to give the exact time of the artifact. In order to obtain the position of the artifact, it is generally necessary to divide the pulse signal into many small segments (generally each segment is 5∼10 seconds). After each artifact is observed, the time of occurrence of the artifact is obtained. Since the length of the segment is 5∼10 seconds, the time resolution of the artifact detection is 5∼10 seconds, by using different weeks of the pulse signal. Starting from the nature of similarity, based on the connectivity of complex networks, a detection method with more accurate detection accuracy and finer time resolution is proposed. Based on this, this article proposes a new pulse signal preprocessing method, which first removes the saturation of the saturation detection method. On this basis, the artifact detection module based on intricate network connectivity is used to remove the artifacts, and finally the adaptive filter filters. The empirical results show that the preprocessing method set out in this study can effectively remove all kinds of noise and remove saturation and artifacts. Under the empirical data, the proposed method has a smaller signal-to-noise ratio and means square error when the convergence speed remains identical. The algorithm proposed in this study is particularly important in smart medical care to detect real-time data.The rest of this article is organized as follows: Section2 describes the pulse signal preprocessing. Proposed saturation removal, artifact removal, and noise removal algorithm are also introduced. In Section 3, the proposed model is formulated and the computational complexity is compared with the existing multi-classifiers. Experimental results are given in Section 4, and Section 5 contains concluding remarks.


## 2. Signal Preprocessing

### 2.1. Saturation Detection and Removal

A saturated pulse signal refers to a signal amplitude that exceeds the maximum or minimum value that the system can represent, such that the space or valley of the pulse signal is flattened. Since a saturated signal loses information when it is recorded, it is generally difficult to recover. In this study, the saturation signal is divided into 2 types according to the degree of saturation: local saturation and general saturation. Figure1(a) and Figure 1(b) show the global saturation of the pulse signal at the top and bottom, correspondingly. We can note that a large number of horizontal segments appear at the top and bottom of the signal, respectively. Figure 1(c) shows a pulse signal with local saturation. It can be observed that the second half of the pulse signal is saturated due to the baseline drift being pulled up. The generation of the global saturation signal is primarily caused by the error of the collector, such as extreme sampling pressure setting or excessive gain setting will cause the signal to saturate. Local saturation is due primarily to the more severe baseline drift.Figure 1
Saturated pulse signal: (a)Pulse signal with saturation at the top, (b)pulse signal with saturation at the bottom, and (c)pulse signal coupled with baseline drift and saturation.
(a)(b)(c)For the saturation detection of signals, this study proposes a saturated signal detection algorithm based on gradient and extremum. The detection of saturated segments mainly depends on two standards. First, if the signalX is saturated at i, then the value of xi should be equal to the maximum or minimum value that the system can express. Second, if the signal X is saturated at i, the gradient of X at i is 0. Since the recorded pulse signal is actually a digital signal after digital-to-analog conversion, the derivative in the second quasi-side can be calculated by difference. In order to make the detection standard correspond to different types of systems, the first criterion is relaxed in this study if the signal X is saturated at i. Then the value of xi should be equal to the maximum or minimum of X. If the signal X is saturated at i, then X should satisfy the following formula:(1)maxX−xi=0,(2)diffX|x=xi=0.From experiments, we find that the condition of (1) is not robust to the voltage fluctuation of the power supply system. In order to make the detection result robust to the voltage fluctuation of the power supply system, we relax the (1) as:(3)maxX−xi≤ε,where ε in the formula is a small positive number, which can generally be set to 2∼3 times of the minimum digital-to-analog conversion precision. Correspondingly, we relax the (2) as follows:(4)diffXx=xi≤ε.In order to avoid the interference of the highest amplitude pulse period in the pulse signal for saturation detection, it is further required that if the signalX is saturated at i, all values of xi and its small neighborhood should satisfy (3) and (4).For the lower end saturation, (1) can be modified to:(5)xi−minX≤ε.The three graphs in Figure2 are the saturation detection results of the pulse signal in Figure 1, where we mark the saturated portion with the ∗ sign.Figure 2
The result of saturation detection of pulse signals in Figure1.
(a)(b)(c)


### 2.2. Detection and Removal of Artifacts

Artifacts are irregular signal segments in the pulse signal. Analogous to saturation, this study also divides artifacts into two categories: local artifacts and global artifacts. Figure3(a) is a pulse signal containing universal artifacts. It can be seen from the figure that the signal of the global artifact does not contain any diagnostic information obtainable, and even the period cannot be resolved. Figure 3(b) is a pulse signal containing local artifacts, and we use the box to draw out the artifacts. It can be seen that the artifact portion signal is significantly abnormal from the shape of the pulse signal before and after it, and approximates the random noise. The causes of native artifacts and global artifacts are generally different. The occurrence of global artifacts is mostly due to the misalignment of the probe position, mainly due to the lack of experience of signal acquisition personnel. In addition, if the patient's brachial artery is farther away from the epidermis, or if the patient's pulse is weaker, the difficulty of collection will increase, and the signal of general artifacts is more likely to take place. The local artifact is a chaotic non-pulse signal presented by a certain segment of the pulse signal due to interference. Figure 3(b) is a pulse signal containing regional artifacts. There are many reasons for indigenous artifacts, such as the acquisition system. The system is unstable due to imperfect circuit design, the patient's rapid body motion such as convulsions, or short period noise of the power supply system, such as the start of another high-power medical equipment in the hospital, causing a short period change in voltage.Figure 3
Pulse signal sampled with artifact: (a)Global artifact and (b)local artifact.
(a)(b)Most of the existing artifact detection methods divide the pulse signal into multiple segments of 5∼10 seconds; extract statistical information such as mean, variance, and sample entropy of the segment; then analyze these statistical features; and use the threshold method to distinguish whether the pulse segment is segmented. [9, 10, 14, 15–17]. In the detection of artifacts, empirical mode decomposition usually separates the high-frequency components of the signal to facilitate the detection of artifacts [11, 12]. However, these methods do not commit the use of the similarity between pulse cycles. This study examines the similarity between pulse cycles. On the one hand, the time resolution of artifact detection can be increased by 5 to 10 seconds to the average pulse period (about 0.7 seconds), while also improving detection accuracy. In this section, an artifact detection module based on complex network connectivity is proposed. For the sake of clarity in the description, the signal in Figure 3(b) is taken as an example. The signal shown in Figure 4 is obtained by noise reduction, period division, and de-baseline drift, and the pulse signal is divided into a plurality of pulse periods and recorded as C1, C2, C3, etc. From the figure, we can see that the pulse signal has a strong periodicity, although there is a certain difference between each cycle, the similarity between cycles is larger than its difference. The pseudo-track segment is a relatively random signal such as C4, C5, C6, C7. The pulse period containing artifacts is neither similar to the normal period nor comparable to other periods containing artifacts. The pulse period containing artifacts is neither parallel to the normal period nor similar to other periods containing artifacts. In addition, although there are some differences between routine pulse periods, this difference is much smaller than the difference between the normal period and the pulse period containing artifacts. Therefore, the pulse period containing artifacts can be detected by the similarity between the comparison periods. In order to eliminate the period containing artifacts, the complex network transformation method is used in this study to map each period of the pulse signal from the time domain to the network domain. We map each cycle of the pulse signal to a node in the network and use the network edge to characterize the similarity between the nodes on the network. If there are edges between the nodes, we think that the two cycles are similar; if there are two nodes, there is no edge between them, indicating that the two cycles are not similar. After mapping the pulse signals to the network domain, the normal pulse periods are connected to each other, and the pulse period containing the artifacts becomes an isolated node. Therefore, we can detect the period containing artifacts by analyzing the connectivity of the complex network obtained by the transformation in Figure 4.Figure 4
Pulse signal after noise reduction and de-baseline drift.To measure the similarity between two cycles, this study uses the phase space distance between two cycles or the correlation coefficient of two pulse periods. Because the pulse signal is continuous and smooth, the phase space distance of the two similar pulse cycles is also small. Generally, the more similar the two pulse cycles are, the greater the correlation coefficient between the two is.(6)Dij=mini=0,1…lj−li1minli,lj∑k=1minli,ljXk−Yk+1,where Xk and Yk are the kth points of periods Ci and Cj, and li and lj are the lengths of periods Ci and Cj. If the phase space distance between periods Ci and Cj is larger, the similarity between periods Ci and Cj is smaller, otherwise the similarity between Ci and Cj is greater. If we use the correlation coefficient as a measure of similarity, the similarity Dij of the periods Ci and Cj can be calculated by (7). It should be noted that if the correlation coefficient is used, then C is opposite to the result of using the phase space distance. The larger the correlation coefficient, the greater the similarity between the two cycle periods Ci and Cj. The smaller the correlation coefficient, the more similar the similarity of the periods Ci and Cj.(7)Dij=maxi=0,1…lj−liCovCi1,li,Cj1+l,li+lVar1,liCj1+l,li+l.In fact, these two metrics are essentially equivalent [14]. This study chooses the correlation coefficient as a measure of similarity. When building this network, we first connect all the nodes (pulse periods) into a fully joined network, using the correlation coefficient between the nodes as the weight on each side, then we set a threshold and delete the network. The weight is less than the edge of the threshold. Thus, changing the network into a binary network. Figure 5 is the network established by the signal in Figure 4. We can see that the period (C5, C6, C7, C8) containing artifacts is isolated, and the normal pulse periods are connected to each other. We can use depth-first traversal or breadth-first traversal to find the largest connected subgraph of this binary network, and then get all the normal pulse cycles, and those isolated nodes are the pulse cycles with artifact. The sequence number of the node indicates the location of the pulse period containing the artifact. Since the segmentation of the pulse signal is split by cycle, the time resolution of our algorithm is similar to the average period of the pulse, about 0.7 seconds.Figure 5
Complex network constructed from signal in Figure4.Since there are definite differences between normal pulse cycles, the maximum connected subgraphs we obtain are generally not fully connected. In fact, detecting artifacts do not require that the maximum connected subgraph of the network be full. We only need routine pulse cycles to connect to each other. Finding a suitable threshold to isolate the pulse period containing artifacts while maintaining the connection between normal pulse periods is important for the detection of artifacts. However, since the pulse period containing artifacts is quite different from the normal pulse period, the threshold can be selected within a relatively large interval. Figure6 shows the tendency of each node degree of the pulse signal in Figure 4 to change with a threshold when setting up a network. In the figure, we use different colors to represent different nodes. From the figure, we can find that the degree of each node gradually decreases as the threshold increases. This is explained by the fact that a larger threshold will delete more edges. At the same time, we can also see that the degree of the node corresponding to the period containing the artifacts decreases faster than the other nodes in the increase of the threshold. For the pulse signal in Figure 4, we can see that when the threshold is higher than 0.45, the degree of the node containing the artifact is reduced to 0, becoming an isolated point. Therefore, any threshold between 0.455 and 0.944 can accurately detect the node containing artifacts.Figure 6
The pulse signal preprocessing framework.This study presents a preprocessing framework and discusses the handling of detected artifacts and saturation interference and the priority of each preprocessing in this section. For the priority of each process in the preprocessing process, generally speaking, according to the difficulty of the processing of the interference, the interference with less interference, easier processing, and difficult to handle postprocessing are addressed first. For high-frequency noise, baseline drift, saturation, and artifacts, the high-frequency noise band is well away from the pulse signal. Therefore, high-frequency noise is the easiest to eliminate of the four types of interference. The removal of baseline drift is proportionately difficult, and sometimes the more severe baseline drift can cause signal saturation, so the removal of baseline drift is harder, and the frequency noise is slightly higher. However, these two kinds of interference are considered relatively easy to handle. Saturation or artifacts are generally difficult to recover, so they have a greater impact and are more difficult to deal with. Among them, the detection of saturation is relatively easy, and the detection of artifacts is relatively difficult. Therefore, the difficulty of removing high-frequency noise, baseline drift, saturation, and artifacts is increasing sequentially. However, the priority of each process in the preprocessing process, in addition to considering the ease of processing of each preprocessing process, also considers the interaction between them. In these four processes, the effects of denoting, de-baseline drift, and artifact detection are less affected. However, since the detection of saturation is mainly the detection of the detection amplitude, it is susceptible to filter and fitting.The noise is removed mainly by low-pass filtering, and here it is primarily removed through Fourier low-pass filtering or wavelet filtering. Both methods will cause the smoothed saturated section to ripple. Removing the baseline drift also affects the detection of saturation. Because the baseline drift is removed, it has a tendency to pull down, or raise part of the pulse period, and makes the straight saturated section tilt. Therefore, it is to a lesser degree had to test the saturation detection module at the forefront, and the detection result is more exact. Accordingly, it becomes less difficult to test the saturation detection module at the forefront, and the detection result is more accurate. Thereby, this article puts the saturation detection process at the forefront of the preprocessing process. According to the processing complexity and the influence of the processing of the signal, the preprocessing pipeline framework proposed in this article is given in Figure6.


### 2.3. Parameterized Integer Coefficient Filtering

The design method of the digital filter is as follows: the filter structure and parameters are designed according to the prior knowledge of the signal, such as the main frequency range; the parameters of the filter are adjusted offline through the measured signal until the satisfactory filtering effect is achieved This method of parameter selection is subjective, and once the filter parameters are fixed, they implement in the hardware system and cannot be changed. However, the pulse signal of the human body is no longer a strict periodic signal, and its frequency range changes as the person's mood and state of motion change. At the same time, as some environmental factors such as light and electromagnetic changes, the frequency and strength of noise also change. In view of the above problems, this article proposes a filtering method that can automatically adjust the filter parameters according to the signal-to-noise ratio change.The principle of the self-adjusting parameter integral coefficient filtering method is shown in Figure7. The full-rate filter is utilized to remove the baseline drift and power frequency interference, and the low-pass filter filters out the high-frequency interference. Then, according to the smoothness of the output calculation result, it is judged whether it meets the requirement, and if not, the parameters of the low-pass filter are adjusted until the requirement is met. The influence of high-frequency interference with the pulse signal is manifested by the burrs attached to the signal, and these burrs have a great impact on the extraction results of further pulse signals. Defining the signal smoothness reflects the extent to which the pulse signal is affected by high-frequency interference According to the characteristics of high-frequency interference in the signal, the signal smoothness (smooth degree, SD) is evaluated by the ratio of the number of signal extreme points and the signal length. For a one-dimensional signal of length n, the number of extreme points is increased, and if the corresponding signal is not smooth, then(8)SD=1−NumEPn−2,where NumEP is the number of extreme points of the signal. The closer the SD is to 1, the smoother the signal is. When SD = 1, the signal is a straight line. The sliding window method is used to calculate the smoothness of the pulse signal, and a threshold is set for the smoothness. It is agreed that when the SD is greater than the threshold, the smoothness of the pulse signal satisfies the requirement. When the smoothness is less than the threshold, the coefficient M and the order n of the low-pass filter are adjusted. The value range of M is set to 5∼10, and the value range of n is set to 1∼5. Each time the window slides, n increases by 1. When the order reaches 5, it is reinitialized to 1, and the M value is increased by 1.Figure 7
Self-adjusting parameter integral coefficient filtering principle.


## 2.1. Saturation Detection and Removal

A saturated pulse signal refers to a signal amplitude that exceeds the maximum or minimum value that the system can represent, such that the space or valley of the pulse signal is flattened. Since a saturated signal loses information when it is recorded, it is generally difficult to recover. In this study, the saturation signal is divided into 2 types according to the degree of saturation: local saturation and general saturation. Figure1(a) and Figure 1(b) show the global saturation of the pulse signal at the top and bottom, correspondingly. We can note that a large number of horizontal segments appear at the top and bottom of the signal, respectively. Figure 1(c) shows a pulse signal with local saturation. It can be observed that the second half of the pulse signal is saturated due to the baseline drift being pulled up. The generation of the global saturation signal is primarily caused by the error of the collector, such as extreme sampling pressure setting or excessive gain setting will cause the signal to saturate. Local saturation is due primarily to the more severe baseline drift.Figure 1
Saturated pulse signal: (a)Pulse signal with saturation at the top, (b)pulse signal with saturation at the bottom, and (c)pulse signal coupled with baseline drift and saturation.
(a)(b)(c)For the saturation detection of signals, this study proposes a saturated signal detection algorithm based on gradient and extremum. The detection of saturated segments mainly depends on two standards. First, if the signalX is saturated at i, then the value of xi should be equal to the maximum or minimum value that the system can express. Second, if the signal X is saturated at i, the gradient of X at i is 0. Since the recorded pulse signal is actually a digital signal after digital-to-analog conversion, the derivative in the second quasi-side can be calculated by difference. In order to make the detection standard correspond to different types of systems, the first criterion is relaxed in this study if the signal X is saturated at i. Then the value of xi should be equal to the maximum or minimum of X. If the signal X is saturated at i, then X should satisfy the following formula:(1)maxX−xi=0,(2)diffX|x=xi=0.From experiments, we find that the condition of (1) is not robust to the voltage fluctuation of the power supply system. In order to make the detection result robust to the voltage fluctuation of the power supply system, we relax the (1) as:(3)maxX−xi≤ε,where ε in the formula is a small positive number, which can generally be set to 2∼3 times of the minimum digital-to-analog conversion precision. Correspondingly, we relax the (2) as follows:(4)diffXx=xi≤ε.In order to avoid the interference of the highest amplitude pulse period in the pulse signal for saturation detection, it is further required that if the signalX is saturated at i, all values of xi and its small neighborhood should satisfy (3) and (4).For the lower end saturation, (1) can be modified to:(5)xi−minX≤ε.The three graphs in Figure2 are the saturation detection results of the pulse signal in Figure 1, where we mark the saturated portion with the ∗ sign.Figure 2
The result of saturation detection of pulse signals in Figure1.
(a)(b)(c)


## 2.2. Detection and Removal of Artifacts

Artifacts are irregular signal segments in the pulse signal. Analogous to saturation, this study also divides artifacts into two categories: local artifacts and global artifacts. Figure3(a) is a pulse signal containing universal artifacts. It can be seen from the figure that the signal of the global artifact does not contain any diagnostic information obtainable, and even the period cannot be resolved. Figure 3(b) is a pulse signal containing local artifacts, and we use the box to draw out the artifacts. It can be seen that the artifact portion signal is significantly abnormal from the shape of the pulse signal before and after it, and approximates the random noise. The causes of native artifacts and global artifacts are generally different. The occurrence of global artifacts is mostly due to the misalignment of the probe position, mainly due to the lack of experience of signal acquisition personnel. In addition, if the patient's brachial artery is farther away from the epidermis, or if the patient's pulse is weaker, the difficulty of collection will increase, and the signal of general artifacts is more likely to take place. The local artifact is a chaotic non-pulse signal presented by a certain segment of the pulse signal due to interference. Figure 3(b) is a pulse signal containing regional artifacts. There are many reasons for indigenous artifacts, such as the acquisition system. The system is unstable due to imperfect circuit design, the patient's rapid body motion such as convulsions, or short period noise of the power supply system, such as the start of another high-power medical equipment in the hospital, causing a short period change in voltage.Figure 3
Pulse signal sampled with artifact: (a)Global artifact and (b)local artifact.
(a)(b)Most of the existing artifact detection methods divide the pulse signal into multiple segments of 5∼10 seconds; extract statistical information such as mean, variance, and sample entropy of the segment; then analyze these statistical features; and use the threshold method to distinguish whether the pulse segment is segmented. [9, 10, 14, 15–17]. In the detection of artifacts, empirical mode decomposition usually separates the high-frequency components of the signal to facilitate the detection of artifacts [11, 12]. However, these methods do not commit the use of the similarity between pulse cycles. This study examines the similarity between pulse cycles. On the one hand, the time resolution of artifact detection can be increased by 5 to 10 seconds to the average pulse period (about 0.7 seconds), while also improving detection accuracy. In this section, an artifact detection module based on complex network connectivity is proposed. For the sake of clarity in the description, the signal in Figure 3(b) is taken as an example. The signal shown in Figure 4 is obtained by noise reduction, period division, and de-baseline drift, and the pulse signal is divided into a plurality of pulse periods and recorded as C1, C2, C3, etc. From the figure, we can see that the pulse signal has a strong periodicity, although there is a certain difference between each cycle, the similarity between cycles is larger than its difference. The pseudo-track segment is a relatively random signal such as C4, C5, C6, C7. The pulse period containing artifacts is neither similar to the normal period nor comparable to other periods containing artifacts. The pulse period containing artifacts is neither parallel to the normal period nor similar to other periods containing artifacts. In addition, although there are some differences between routine pulse periods, this difference is much smaller than the difference between the normal period and the pulse period containing artifacts. Therefore, the pulse period containing artifacts can be detected by the similarity between the comparison periods. In order to eliminate the period containing artifacts, the complex network transformation method is used in this study to map each period of the pulse signal from the time domain to the network domain. We map each cycle of the pulse signal to a node in the network and use the network edge to characterize the similarity between the nodes on the network. If there are edges between the nodes, we think that the two cycles are similar; if there are two nodes, there is no edge between them, indicating that the two cycles are not similar. After mapping the pulse signals to the network domain, the normal pulse periods are connected to each other, and the pulse period containing the artifacts becomes an isolated node. Therefore, we can detect the period containing artifacts by analyzing the connectivity of the complex network obtained by the transformation in Figure 4.Figure 4
Pulse signal after noise reduction and de-baseline drift.To measure the similarity between two cycles, this study uses the phase space distance between two cycles or the correlation coefficient of two pulse periods. Because the pulse signal is continuous and smooth, the phase space distance of the two similar pulse cycles is also small. Generally, the more similar the two pulse cycles are, the greater the correlation coefficient between the two is.(6)Dij=mini=0,1…lj−li1minli,lj∑k=1minli,ljXk−Yk+1,where Xk and Yk are the kth points of periods Ci and Cj, and li and lj are the lengths of periods Ci and Cj. If the phase space distance between periods Ci and Cj is larger, the similarity between periods Ci and Cj is smaller, otherwise the similarity between Ci and Cj is greater. If we use the correlation coefficient as a measure of similarity, the similarity Dij of the periods Ci and Cj can be calculated by (7). It should be noted that if the correlation coefficient is used, then C is opposite to the result of using the phase space distance. The larger the correlation coefficient, the greater the similarity between the two cycle periods Ci and Cj. The smaller the correlation coefficient, the more similar the similarity of the periods Ci and Cj.(7)Dij=maxi=0,1…lj−liCovCi1,li,Cj1+l,li+lVar1,liCj1+l,li+l.In fact, these two metrics are essentially equivalent [14]. This study chooses the correlation coefficient as a measure of similarity. When building this network, we first connect all the nodes (pulse periods) into a fully joined network, using the correlation coefficient between the nodes as the weight on each side, then we set a threshold and delete the network. The weight is less than the edge of the threshold. Thus, changing the network into a binary network. Figure 5 is the network established by the signal in Figure 4. We can see that the period (C5, C6, C7, C8) containing artifacts is isolated, and the normal pulse periods are connected to each other. We can use depth-first traversal or breadth-first traversal to find the largest connected subgraph of this binary network, and then get all the normal pulse cycles, and those isolated nodes are the pulse cycles with artifact. The sequence number of the node indicates the location of the pulse period containing the artifact. Since the segmentation of the pulse signal is split by cycle, the time resolution of our algorithm is similar to the average period of the pulse, about 0.7 seconds.Figure 5
Complex network constructed from signal in Figure4.Since there are definite differences between normal pulse cycles, the maximum connected subgraphs we obtain are generally not fully connected. In fact, detecting artifacts do not require that the maximum connected subgraph of the network be full. We only need routine pulse cycles to connect to each other. Finding a suitable threshold to isolate the pulse period containing artifacts while maintaining the connection between normal pulse periods is important for the detection of artifacts. However, since the pulse period containing artifacts is quite different from the normal pulse period, the threshold can be selected within a relatively large interval. Figure6 shows the tendency of each node degree of the pulse signal in Figure 4 to change with a threshold when setting up a network. In the figure, we use different colors to represent different nodes. From the figure, we can find that the degree of each node gradually decreases as the threshold increases. This is explained by the fact that a larger threshold will delete more edges. At the same time, we can also see that the degree of the node corresponding to the period containing the artifacts decreases faster than the other nodes in the increase of the threshold. For the pulse signal in Figure 4, we can see that when the threshold is higher than 0.45, the degree of the node containing the artifact is reduced to 0, becoming an isolated point. Therefore, any threshold between 0.455 and 0.944 can accurately detect the node containing artifacts.Figure 6
The pulse signal preprocessing framework.This study presents a preprocessing framework and discusses the handling of detected artifacts and saturation interference and the priority of each preprocessing in this section. For the priority of each process in the preprocessing process, generally speaking, according to the difficulty of the processing of the interference, the interference with less interference, easier processing, and difficult to handle postprocessing are addressed first. For high-frequency noise, baseline drift, saturation, and artifacts, the high-frequency noise band is well away from the pulse signal. Therefore, high-frequency noise is the easiest to eliminate of the four types of interference. The removal of baseline drift is proportionately difficult, and sometimes the more severe baseline drift can cause signal saturation, so the removal of baseline drift is harder, and the frequency noise is slightly higher. However, these two kinds of interference are considered relatively easy to handle. Saturation or artifacts are generally difficult to recover, so they have a greater impact and are more difficult to deal with. Among them, the detection of saturation is relatively easy, and the detection of artifacts is relatively difficult. Therefore, the difficulty of removing high-frequency noise, baseline drift, saturation, and artifacts is increasing sequentially. However, the priority of each process in the preprocessing process, in addition to considering the ease of processing of each preprocessing process, also considers the interaction between them. In these four processes, the effects of denoting, de-baseline drift, and artifact detection are less affected. However, since the detection of saturation is mainly the detection of the detection amplitude, it is susceptible to filter and fitting.The noise is removed mainly by low-pass filtering, and here it is primarily removed through Fourier low-pass filtering or wavelet filtering. Both methods will cause the smoothed saturated section to ripple. Removing the baseline drift also affects the detection of saturation. Because the baseline drift is removed, it has a tendency to pull down, or raise part of the pulse period, and makes the straight saturated section tilt. Therefore, it is to a lesser degree had to test the saturation detection module at the forefront, and the detection result is more exact. Accordingly, it becomes less difficult to test the saturation detection module at the forefront, and the detection result is more accurate. Thereby, this article puts the saturation detection process at the forefront of the preprocessing process. According to the processing complexity and the influence of the processing of the signal, the preprocessing pipeline framework proposed in this article is given in Figure6.


## 2.3. Parameterized Integer Coefficient Filtering

The design method of the digital filter is as follows: the filter structure and parameters are designed according to the prior knowledge of the signal, such as the main frequency range; the parameters of the filter are adjusted offline through the measured signal until the satisfactory filtering effect is achieved This method of parameter selection is subjective, and once the filter parameters are fixed, they implement in the hardware system and cannot be changed. However, the pulse signal of the human body is no longer a strict periodic signal, and its frequency range changes as the person's mood and state of motion change. At the same time, as some environmental factors such as light and electromagnetic changes, the frequency and strength of noise also change. In view of the above problems, this article proposes a filtering method that can automatically adjust the filter parameters according to the signal-to-noise ratio change.The principle of the self-adjusting parameter integral coefficient filtering method is shown in Figure7. The full-rate filter is utilized to remove the baseline drift and power frequency interference, and the low-pass filter filters out the high-frequency interference. Then, according to the smoothness of the output calculation result, it is judged whether it meets the requirement, and if not, the parameters of the low-pass filter are adjusted until the requirement is met. The influence of high-frequency interference with the pulse signal is manifested by the burrs attached to the signal, and these burrs have a great impact on the extraction results of further pulse signals. Defining the signal smoothness reflects the extent to which the pulse signal is affected by high-frequency interference According to the characteristics of high-frequency interference in the signal, the signal smoothness (smooth degree, SD) is evaluated by the ratio of the number of signal extreme points and the signal length. For a one-dimensional signal of length n, the number of extreme points is increased, and if the corresponding signal is not smooth, then(8)SD=1−NumEPn−2,where NumEP is the number of extreme points of the signal. The closer the SD is to 1, the smoother the signal is. When SD = 1, the signal is a straight line. The sliding window method is used to calculate the smoothness of the pulse signal, and a threshold is set for the smoothness. It is agreed that when the SD is greater than the threshold, the smoothness of the pulse signal satisfies the requirement. When the smoothness is less than the threshold, the coefficient M and the order n of the low-pass filter are adjusted. The value range of M is set to 5∼10, and the value range of n is set to 1∼5. Each time the window slides, n increases by 1. When the order reaches 5, it is reinitialized to 1, and the M value is increased by 1.Figure 7
Self-adjusting parameter integral coefficient filtering principle.


## 3. Algorithm Simulation and Comparison

### 3.1. Experimental Data

Experimental data are divided into simulation signal and measured signal in Figure8. The simulated pulse signal can be used as a clean signal to judge whether the filtering result is good or bad; the measured signal includes noise and interference signals, and pulse signals. The noise signal is added to the simulated pulse signal to simulate the actual pulse signal, and the measured pulse signal is used to verify the actual filtering ability of the filtering method.In 1994, Qian Weili and others of Lanzhou University proposed to use the Gaussian function to synthesize pulse waves and establish a pulse signal model [9]. Many scholars have demonstrated the Gaussian function synthetic pulse wave, and the results show that the three Gaussian functions can effectively describe the pulse waveform morphology [10,11]. A pulse wave is recorded as pwk. According to the characteristics of the pulse signal, the clean pulse wave is synthesized by three Gaussian functions, corresponding to the main wave of the actual pulse wave, the pre-pulsation front wave, and the heavy beat wave. The expression is as follows:(9)pwk=∑j=13Ajexp−k−pj2/bjk∈0,1,where Aj determines the height of the Gaussian function image, pj determines the peak position of the image, and bj determines the image width. A1=0.8, p1=0.25, b1=0.012; A2=0.5, p2=0.45, b2=0.010; and A3=0.5; p3=0.70, b3=0.030. If the interval between data points is 1/500, the sampling period of the actual digital signal is simulated, and the corresponding sampling frequency is 500 Hz. For the sake of simplicity of description, the sampling period and the sampling frequency are directly referred to below. A periodic pulse wave is shown in the sub-figure of Figure 8(a). As can be seen from the figure, the synthesized pulse signal contains the basic characteristics of the pulse signal, and the pulse signals of different pulses can be simulated by changing the parameters in (9). A single periodic pulse wave generated by (9) is extended to generate a clean signal that can simulate the actual pulse signal. Recorded as CPPGi, i=1,2,…,N, N is the signal length. The signal is shown in the sub-figure of Figure 8(b). The noise signal [12] provided by the MIT-BIH/PhysioNet/Noise Stress Test database is used to add a clean pulse signal to simulate the actual pulse signal. The database noise signal includes baseline drift (data name: bw), myoelectric interference (data name: ma), and power frequency interference and random noise contained in bw and ma. The signal sampling frequency is 250 Hz and the sampling length is 3 hours. In order to eliminate the influence of the difference between the amplitude of the simulated signal and the noise signal, the clean signal is normalized (average is 0 and standard deviation is 1) before adding noise. The formula is as follows:(10)si=CPPGi−meanCPPGistdCPPGi,where meanCPPGi and stdCPPGi are the mean and standard deviation of CPPGi, respectively. si is the normalized pulse signal. In the experiment, it is used as a clean signal (true value signal) to calculate the accuracy of the filtering result. Then, the noise signal of the same length as the clean signal is intercepted and resampled, so that the sampling frequency is the same as the clean pulse signal. The noise level is adjusted by multiplying the noise signal by a different coefficient before adding the pulse signal si. Note that the noise signal is ni, then:(11)ni=a⋅bwi+b⋅mai,where bwi is the baseline drift, mai is the myoelectric interference, and a and b are the noise figure. ni is added to si to generate noise and interfere with the contaminated pulse signal. The signal-to-noise ratio (SNR) is calculated by the following equation:(12)SNR=10lgstsstn,where sts is the variance of the clean signal si and stn is the noise and interference variance. Pulse signals of different SNRs are generated by adjusting the noise figure a , b. Pulse signals with different SNRs are generated for different noise figures and are shown in Table 1.Figure 8
Simulated pulse signal synthesis: (a) single cycle pulse wave synthesis and (b) pulse signal synthesis.
(a)(b)Table 1
Noise figure and signal-to-noise ratio.
aBSNR (dB)0.0050.001112.60.0070.00119.560.0110.00116.580.0120.00123.6


### 3.2. Evaluation

From the MIT-BIH/Phsionet/Compution in cardiology challenge 2014 database, 99 groups of physiological signals (data name: 101m-199 m) were selected as measured data, and each group of data contained ECG, pulse, blood pressure, respiratory and EEG signals, and signals. The sampling frequency is 250 Hz and the sampling time is 10 min. At the same time, the pulse signal detection and processing system developed by our research group collects the human body pulse signal. The signal sampling frequency is 500 Hz and the sampling time is 10 min. The proposed method is used to measure the pulse signal and verify the actual filtering effect of the method.


## 3.1. Experimental Data

Experimental data are divided into simulation signal and measured signal in Figure8. The simulated pulse signal can be used as a clean signal to judge whether the filtering result is good or bad; the measured signal includes noise and interference signals, and pulse signals. The noise signal is added to the simulated pulse signal to simulate the actual pulse signal, and the measured pulse signal is used to verify the actual filtering ability of the filtering method.In 1994, Qian Weili and others of Lanzhou University proposed to use the Gaussian function to synthesize pulse waves and establish a pulse signal model [9]. Many scholars have demonstrated the Gaussian function synthetic pulse wave, and the results show that the three Gaussian functions can effectively describe the pulse waveform morphology [10,11]. A pulse wave is recorded as pwk. According to the characteristics of the pulse signal, the clean pulse wave is synthesized by three Gaussian functions, corresponding to the main wave of the actual pulse wave, the pre-pulsation front wave, and the heavy beat wave. The expression is as follows:(9)pwk=∑j=13Ajexp−k−pj2/bjk∈0,1,where Aj determines the height of the Gaussian function image, pj determines the peak position of the image, and bj determines the image width. A1=0.8, p1=0.25, b1=0.012; A2=0.5, p2=0.45, b2=0.010; and A3=0.5; p3=0.70, b3=0.030. If the interval between data points is 1/500, the sampling period of the actual digital signal is simulated, and the corresponding sampling frequency is 500 Hz. For the sake of simplicity of description, the sampling period and the sampling frequency are directly referred to below. A periodic pulse wave is shown in the sub-figure of Figure 8(a). As can be seen from the figure, the synthesized pulse signal contains the basic characteristics of the pulse signal, and the pulse signals of different pulses can be simulated by changing the parameters in (9). A single periodic pulse wave generated by (9) is extended to generate a clean signal that can simulate the actual pulse signal. Recorded as CPPGi, i=1,2,…,N, N is the signal length. The signal is shown in the sub-figure of Figure 8(b). The noise signal [12] provided by the MIT-BIH/PhysioNet/Noise Stress Test database is used to add a clean pulse signal to simulate the actual pulse signal. The database noise signal includes baseline drift (data name: bw), myoelectric interference (data name: ma), and power frequency interference and random noise contained in bw and ma. The signal sampling frequency is 250 Hz and the sampling length is 3 hours. In order to eliminate the influence of the difference between the amplitude of the simulated signal and the noise signal, the clean signal is normalized (average is 0 and standard deviation is 1) before adding noise. The formula is as follows:(10)si=CPPGi−meanCPPGistdCPPGi,where meanCPPGi and stdCPPGi are the mean and standard deviation of CPPGi, respectively. si is the normalized pulse signal. In the experiment, it is used as a clean signal (true value signal) to calculate the accuracy of the filtering result. Then, the noise signal of the same length as the clean signal is intercepted and resampled, so that the sampling frequency is the same as the clean pulse signal. The noise level is adjusted by multiplying the noise signal by a different coefficient before adding the pulse signal si. Note that the noise signal is ni, then:(11)ni=a⋅bwi+b⋅mai,where bwi is the baseline drift, mai is the myoelectric interference, and a and b are the noise figure. ni is added to si to generate noise and interfere with the contaminated pulse signal. The signal-to-noise ratio (SNR) is calculated by the following equation:(12)SNR=10lgstsstn,where sts is the variance of the clean signal si and stn is the noise and interference variance. Pulse signals of different SNRs are generated by adjusting the noise figure a , b. Pulse signals with different SNRs are generated for different noise figures and are shown in Table 1.Figure 8
Simulated pulse signal synthesis: (a) single cycle pulse wave synthesis and (b) pulse signal synthesis.
(a)(b)Table 1
Noise figure and signal-to-noise ratio.
aBSNR (dB)0.0050.001112.60.0070.00119.560.0110.00116.580.0120.00123.6


## 3.2. Evaluation

From the MIT-BIH/Phsionet/Compution in cardiology challenge 2014 database, 99 groups of physiological signals (data name: 101m-199 m) were selected as measured data, and each group of data contained ECG, pulse, blood pressure, respiratory and EEG signals, and signals. The sampling frequency is 250 Hz and the sampling time is 10 min. At the same time, the pulse signal detection and processing system developed by our research group collects the human body pulse signal. The signal sampling frequency is 500 Hz and the sampling time is 10 min. The proposed method is used to measure the pulse signal and verify the actual filtering effect of the method.


## 4. Experimental Results and Discussion

In the experiment, the mean square error (MSE) and the signal-to-noise ratio (SNR) are used to evaluate the filtering effect. The MSE reflects the overall similarity of the two signals, and the SNR reflects the noise level in the signal, where SNR is defined as equation (13) and MSE is defined as(13)MSE=1N∑i=1Nsi−yi2,where yi is the filtered signal, si is the clean signal, and N is the signal length. The smaller the MSE value, the better the filtering effect. Self-adjusting parameter integer coefficient filtering method: according to the principle of self-adjusting parameter integral coefficient filtering method, the parameters of the integral coefficient notch filter need to be set to remove the baseline drift and power frequency interference in the signal. Compared to other interferences, the baseline drift and power frequency interference frequency range is small, and it can be filtered out by a fixed parameter integer coefficient filter.Since the simulated pulse signal data point interval is 1/500, the actual pulse signal sampling frequency is 500 Hz in Figure9. To filter out the signal components of 50 Hz and its integer multiples, according to the trap design principle, f0=50Hz, then, P = 11. In the formula, the values of n and R determine the steepness of the stop band. The larger the value is, the steeper the filter is, the better the performance of the filter is, but the delay increases and the amount of filtering increases. Ensure that the gain Q is an integer and make the value a positive integer power of 2, so that in the process of implementation, without multiplying the coefficient by the sampling point, the sampling operation can be directly performed by shifting the sampling point. Therefore, as long as Q is adjusted, the filter performance can be changed. After a lot of experiments, this article takes n  = 2, Q  = 5, and R  = 60, and the system transfer function and frequency response of the integral coefficient notch filter are obtained as follows:(14)HNCHz=z−70−1−z−808⋅1−z−102,HNCHejw=e−70jw1−1Q⋅sin280w/2sinn10w/2.Figure 9
Frequency response of the trap.The amplitude and phase response of the filter are shown in Figure10. It can be seen from the amplitude-frequency diagram that there is a stop band at the expected frequency. The phase-frequency diagram shows that the filter in the passband is linear to meet the filtering requirements.Figure 10
Frequency response of the low-pass filter.For low-pass filters, the parameters are adjusted based on the smoothness of the filtered signal. Equation (10) is used to adjust the cutoff frequency of the low-pass filter, which ranges from 5 to 10. The frequency of the simulated pulse signal is 500 Hz, and the cutoff frequency ranges from 100 Hz to 50 Hz. The parameter is used to adjust the steepness of the passband, which ranges from 1 to 5. The purpose of self-tuning parameter filtering is to preserve the active components in the pulse signal as much as possible while filtering out noise. Although the main frequency range of the pulse signal is from 0 Hz to 40 Hz, retaining its high-frequency components may be useful for later signal analysis. Therefore, the cutoff frequency varies from 100 Hz to 50 Hz. In special cases, when M  = 5, n  = 1, and the system transfer function and frequency response of the low-pass filter are(15)Hz=1−z−55⋅1−z−1,HLPejw=15⋅e−4jw/2⋅sin5w/2sinw/2.In order to reduce the influence of noise selection on the performance of the method, the noise data in the MIT-BIH noise database are randomly intercepted for a total of 100 segments. The clean pulse signal generated by the modeling is added and filtered by four methods. The results are shown in Table2. As far as MSE is concerned, the MSE of the EMD decomposition method has the smallest mean value, followed by the self-adjusting parameter integer coefficient filtering proposed in this study, mathematical morphology filtering, and finally the integer coefficient filtering effect, which is the worst. However, the variance of EMD decomposition MSE is large, that is, sometimes the filtering effect is the worst, up to 0.298. When the noise changes abruptly, the EMD decomposition is aliased, which results in information loss and a poor filtering effect. Similarly, the analysis of SNR yields the same results. The intrinsic coefficient filtering takes the least time to run, followed by the self-adjusting parameter elemental coefficients filtering, and the morphological filtering takes the longest time to run. Because the whole coefficient filtering is realized by the difference equation iteration, and the coefficient is the integer, it takes the smallest time. Compared with the integral coefficient filtering, the self-tuning parameter needs to calculate the smoothness of the signal and adjust the parameters of the filter, which is naturally time-consuming than the integer coefficient filtering. It is long, but it takes a short time compared to EMD decomposition and morphologic filtering. Because EMD decomposition requires reiterated iterative decomposition, which takes a lot of time, morphological filtering requires repeated calculations of the pulse signal and structural elements, and the amount of computations is proportional to the length of the organizational element. Considering comprehensively, the proposed self-adjusting parameter integral coefficient filtering method can accurately and quickly achieve pulse signal filtering.Table 2
Performance comparison of four pulse signal filtering methods.
MethodMSESNR (dB)TIME (s)EMD0.123± 0.17816.582± 4.24210.79± 1.691Whole coefficient0.244± 0.00113.795± 0.0150.032± 0.005Morphological0.202± 0.00115.810± 0.0583.021± 1.101The methods proposed0.149± 0.00316.664± 0.1800.062± 0.002


## 5. Conclusion

Pulse signal preprocessing is the core technology of pulse signal diagnosis. This study proposes a preprocessing method based on deep learning. The proposed preprocessing algorithm effectively reduced interference such as the baseline offset, while removing saturation and artifacts and maintaining the distortion of the pulse signal state. A gradient and extreme-based saturation algorithm is designed to remove saturation. The artifact detection module based on complex network connectivity is used to remove signal artifacts. Finally, adaptive filters are used to remove noise such as baseline drift. In the same experimental environment, the current popular concentrating algorithm is compared. The empirical results show that the proposed algorithm can achieve a small mean square error of 0.148 and a convergence time of 0.062 seconds under a similar SNR of 16.5 dB, which is shorter than other algorithms. The method combines artificial intelligence with pulse signal classification and recognition and can be used in a new type of cardiac-assisted diagnosis system. The pulse signal is collected by the wearable terminal and transmitted to the pulse cloud computing platform in real time, through data transformation, adaptive demising, and signal. Preprocessing such as identification, segmentation, etc., based on this algorithm, the disease is diagnosed in real time and returned to the client. This deep learning-based pulse signal preprocessing method can be combined with wearable devices, Internet of Things, and wireless communication technologies to further promote the development of new smart medical care, extend disease prevention, and monitor and diagnose out-of-home scenarios such as homes and nursing homes. To supplement the shortcomings for areas with weak medical conditions and provide efficient services for patients, which can greatly save medical resources, refer to [15–17].



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*Source: 4729105-2022-07-08.xml*