PPG signal denoising method based on CEMDAN combined wavelet threshold
By combining CEMDAN with wavelet thresholding, the PPG signal is decomposed into IMF components of various orders. The noise interference problem in the PPG signal is solved by using correlation coefficient evaluation and wavelet thresholding for denoising, thereby improving the signal quality and accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUNAN INSTITUTE OF SCIENCE AND TECHNOLOGY
- Filing Date
- 2023-12-05
- Publication Date
- 2026-04-21
AI Technical Summary
Existing technologies are unable to effectively remove noise interference from PPG signals, especially power frequency interference, electromyographic interference, and baseline drift, which leads to unreliable data in subsequent physiological health assessments.
The method of combining CEMDAN and wavelet thresholding is adopted. The PPG signal is decomposed into IMF components of various orders by the CEEMDAN algorithm. The correlation coefficient evaluation standard is used to distinguish between correlated and uncorrelated components. The noise in the uncorrelated components is removed by wavelet thresholding, and the effective information is retained.
It effectively reduces noise interference in PPG signals, retains more effective information, improves signal quality and accuracy, maintains the consistency of signal shape and dynamic changes, and is suitable for different noise environments.
Smart Images
Figure CN121890960A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of photoplethysmography (PPG) denoising, and in particular to a PPG signal denoising method based on CEMDAN combined with wavelet thresholding. Background Technology
[0002] Pulse signals contain rich physiological and pathological information about the human body. To date, pulse waves have been applied in various human health monitoring scenarios, including blood pressure monitoring, anesthesia depth monitoring, preeclampsia detection, and emotion recognition. Pulse signals are low-frequency and weak signals. Figure 1 The original PPG signal spectrum contains effective information primarily distributed in the 0–10 Hz frequency band. During acquisition, this band is susceptible to various noise interferences. The magnitude of the signal acquired by the sensor is only a few millivolts, easily submerged in various noises. The acquired pulse signals typically contain the following noises: 1) power frequency interference at a fixed frequency of 50 Hz; 2) electromyographic interference caused by limb and muscle tremors, with a wide frequency range; 3) baseline drift caused by human respiration or movement, with a frequency less than 1 Hz. If noise cannot be effectively filtered out, it will be difficult to use this data as valid support in subsequent physiological health assessments. Because PPG signals are very weak during acquisition and contain multiple noise sources, effective noise removal is difficult.
[0003] Therefore, a PPG signal denoising method based on CEMDAN combined with wavelet thresholding is provided. Summary of the Invention
[0004] The purpose of this invention is to provide a PPG signal denoising method based on CEMDAN combined with wavelet thresholding, which overcomes the shortcomings of existing denoising methods. The original PPG signal is decomposed using CEMDAN to obtain the IMF components of each order of the PPG signal. The irrelevant components are removed by combining wavelet thresholding, and the effective components are retained. The effectiveness of the denoising method is verified by real-world acquisition of PPG data through a self-designed pulse signal acquisition system.
[0005] To achieve the above objectives, this invention provides a PPG signal denoising method based on CEMDAN combined with wavelet thresholding, comprising the following steps:
[0006] Step 1: Set up the detection platform and collect photoplethysmography (PPG) signals;
[0007] Step 2: Use the CEEMDAN algorithm to decompose the PPG signal and obtain the Intrinsic Mode Components (IMFs) of each order of the PPG signal;
[0008] Step 3: Calculate the correlation coefficient r of each intrinsic mode component (IMF). Based on the evaluation criteria of the correlation coefficient, evaluate the correlation between each IMF and the original signal, select the discrimination value, and classify them into correlated IMF and uncorrelated IMF based on the discrimination value.
[0009] Step 4: Perform wavelet decomposition on the uncorrelated intrinsic mode components (IMFs), set a wavelet threshold to remove noise from the uncorrelated intrinsic mode components (IMFs), and obtain the denoised uncorrelated intrinsic mode components.
[0010] Step 5: Reconstruct the signal to obtain the denoised signal.
[0011] Preferably, in step one, the detection platform includes seven modules: a pulse acquisition module, a preamplifier module, a 50Hz notch filter module, a 10Hz low-pass filter module, a main amplifier module, an AD conversion module, and an STM32 main control module. The detection platform records data at a sampling frequency of 200Hz.
[0012] Preferably, in step two, the specific steps for decomposing the PPG signal using the CEEMDAN algorithm are as follows:
[0013] In the CEEMDAN process, β is defined. i Let n be the i-th noise figure. i It is Gaussian white noise with a mean of 0 and a variance of 1;
[0014] S1: The original PPG signal is superimposed with Gaussian white noise to form the signal to be decomposed, as shown in the following formula:
[0015] x (i) =x+β0n i (1)
[0016] In the above formula, x is the original PPG signal, and then x (i) First-order IMF components were obtained by performing Empirical Mode Decomposition (EMD). The decomposition expression of the remaining component r1(t) is as follows:
[0017]
[0018] In the above formula, This represents the first intrinsic mode component after EMD decomposition of the original PPG signal and Gaussian white noise. The final first-order intrinsic mode component is obtained by repeating EMD decomposition on the original signal N times and taking the average. The expression is as follows:
[0019]
[0020] S2: Calculate the first-order remainder r1(t), where r1(t) is the remainder after removing the first-order remainder from the original signal. The remaining part is expressed as follows:
[0021]
[0022] S3: Obtain the second-order intrinsic mode components and add noise β1n to the remainder term r1(t). i The signal to be decomposed is obtained as r1(t) + β1E1(n). (i) ), and then use empirical mode decomposition to re-evaluate r1(t)+β1E1(n) (i) Decompose N times to obtain N first-order IMF components of the PPG signal. That is, the second-order IMF component of the original PPG signal, for the obtained N... The average value of the components is obtained Its expression is as follows:
[0023]
[0024] S4: Calculate the residual component r of order k. k (t), whose expression is as follows:
[0025]
[0026] S5: r is analyzed through empirical mode decomposition. k (t)+β k n i After processing, the (k+1)th order IMF component of the original signal is obtained as follows: For r k (t)+β k n i After decomposing N times and averaging, the final k+1 order IMF component is obtained. The expression is as follows:
[0027]
[0028] S6: Repeat steps S4 and S5 until the next-order IMF component is obtained. This iterative process will continue until the termination condition of the maximum number of iterations is met.
[0029] The formula after decomposing the original function is as follows:
[0030]
[0031] In the above formula, R represents a series of IMF components. k (t) is the final remainder.
[0032] Preferably, in step three, the evaluation criteria using the correlation coefficient are as follows:
[0033] When |r| < 0.3, it is uncorrelated; when 0.3 ≤ |r| < 0.5, it is poorly correlated; when 0.5 ≤ |r| < 0.8, it is significantly correlated; when |r| ≥ 0.8, it is highly correlated. The distinguishing value between correlated and uncorrelated IMF components should be set according to the evaluation criteria.
[0034] Preferably, in step three, the formula for calculating the correlation coefficient of each intrinsic mode component (IMF) is as follows:
[0035]
[0036] In the above formula, X(t) is the noisy PPG signal. The average value of the noisy PPG signal. Let be the mean of the i-th order IMF component.
[0037] Preferably, in step four, the specific process of setting a wavelet threshold to remove noise from the unrelated intrinsic mode components (IMFs) is as follows:
[0038] The original signal is transformed into the wavelet domain for processing to obtain wavelet coefficients at different scales and frequencies. Simulation experiments are conducted to determine the wavelet basis and the number of decomposition layers. For PPG signals, the optimal number of decomposition layers is set to 3, and the optimal wavelet basis is set to db4. Based on the wavelet basis and the number of decomposition layers, soft thresholding or hard thresholding functions are used for denoising.
[0039] Preferably, in step five, the formula for reconstructing the signal is as follows:
[0040]
[0041] In the above formula, It is a combination of relevant intrinsic modal components and residuals. It is a combination of unrelated intrinsic mode components after wavelet thresholding for denoising.
[0042] Therefore, the PPG signal denoising method based on CEMDAN combined wavelet thresholding, which adopts the above method, has the following advantages:
[0043] (1) In this invention, the method used can effectively reduce noise interference in PPG signals and retain more effective information, thereby improving the quality and accuracy of the signal. CEMDAN, as an adaptive decomposition method, can adaptively extract intrinsic mode functions and residual terms according to the characteristics of the signal, thereby better separating noise components.
[0044] (2) In this invention, the PPG signal denoising method based on CEMDAN reduces noise while preserving the important features of the original signal as much as possible. Through noise estimation and signal reconstruction steps, this method can reduce the distortion of the PPG signal and maintain the consistency of the signal's shape and dynamic changes.
[0045] (3) In this invention, for the relevant IMF components and unrelated IMF components obtained by CEEMDAN decomposition, the technical solution of this invention does not directly discard the unrelated components, but adopts a noise reduction method based on wavelet transform to retain the effective components in the unrelated components as much as possible, and performs signal reconstruction together, so that the reconstructed signal has sufficient effective components.
[0046] (4) In this invention, CEMDAN, as an adaptive decomposition method, can be adaptively adjusted according to different signal characteristics and noise conditions. This makes the PPG signal denoising method based on CEMDAN flexible and applicable to different types of PPG signals and noise environments.
[0047] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description
[0048] Figure 1 This is a flowchart of a PPG signal denoising method based on CEMDAN combined wavelet thresholding according to the present invention;
[0049] Figure 2 This is a flowchart of the circuit framework of the detection platform in the PPG signal denoising method based on CEMDAN and wavelet thresholding according to the present invention.
[0050] Figure 3 The original PPG signal spectrum is shown in the PPG signal denoising method based on CEMDAN joint wavelet thresholding of the present invention.
[0051] Figure 4 This is a diagram illustrating the components of the PPG signal in the PPG signal denoising method based on CEMDAN joint wavelet thresholding according to the present invention.
[0052] Figure 5 This is a diagram of the IMF components containing residuals after CEMDAN decomposition in a PPG signal denoising method based on CEMDAN joint wavelet thresholding according to the present invention.
[0053] Figure 6 This is a wavelet decomposition layer analysis diagram in the PPG signal denoising method based on CEMDAN joint wavelet thresholding of the present invention;
[0054] Figure 7This is a diagram showing the analysis of different wavelet bases in a PPG signal denoising method based on CEMDAN joint wavelet thresholding according to the present invention.
[0055] Figure 8 This is a waveform comparison diagram of photoplethysmography (PPG) before and after PPG denoising based on CEMDAN combined wavelet thresholding, according to the present invention. Detailed Implementation
[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.
[0057] Example
[0058] like Figure 1 This invention discloses a PPG signal denoising method based on CEMDAN combined with wavelet thresholding, comprising the following steps:
[0059] Step 1: Set up the detection platform and collect photoplethysmography (PPG) signals;
[0060] like Figure 2 This is a circuit diagram of the pulse processing system. It uses an HK-07C infrared pulse sensor paired with a self-designed pulse processing circuit to acquire optical pulse waveform PPG data. The detection platform includes seven modules: a pulse acquisition module, a preamplifier module, a 50Hz notch filter module, a 10Hz low-pass filter module, a main amplifier module, an AD conversion module, and an STM32 main control module. The detection platform selects young people aged 20 to 25 as the data acquisition subjects. This age group is considered to be a period of relatively stable cardiovascular activity, which helps to more purely reflect the inherent properties of the PPG signal. All data is recorded at a sampling frequency of 200Hz to ensure that subtle changes in pulse fluctuations are captured at high resolution.
[0061] Because the pulse signals acquired by the sensor have small amplitudes, are prone to interference, and have a wide frequency range, they require multiple processing steps to obtain a clean pulse signal. After obtaining the raw pulse signal from the pulse sensor, it is pre-amplified, passed through a notch filter to remove power frequency interference, and then low-pass filtered. It is then amplified again by a programmable amplifier (main amplifier) for AD acquisition by the main control module. Finally, it is transmitted via serial port to a PC for processing and analysis, resulting in the original PPG signal spectrum, as shown below. Figure 3 As shown;
[0062] Step 2: Use the CEEMDAN algorithm to decompose the PPG signal and obtain the Intrinsic Mode Components (IMFs) of each order of the PPG signal;
[0063] In the CEEMDAN process, β is defined. i Let n be the i-th noise figure. i It is Gaussian white noise with a mean of 0 and a variance of 1;
[0064] S1: The original PPG signal is superimposed with Gaussian white noise to form the signal to be decomposed, as shown in the following formula:
[0065] x (i) =x+β0n i (1)
[0066] In the above formula, x is the original PPG signal, and then x (i) First-order IMF components were obtained by performing Empirical Mode Decomposition (EMD). The decomposition expression of the remaining component r1(t) is as follows:
[0067]
[0068] In the above formula, this component This represents the first intrinsic mode component after the original PPG signal is superimposed with Gaussian white noise. The final first-order intrinsic mode component is obtained by repeating empirical mode decomposition of the original signal N times and taking the average value. The expression is as follows:
[0069]
[0070] S2: Calculate the first-order remainder r1(t), where r1(t) can be considered as the term removed from the original signal. The remaining part is expressed as follows:
[0071]
[0072] S3: Obtain the second-order intrinsic mode components and add noise β1n to the remainder term r1(t). i The signal to be decomposed is obtained as r1(t) + β1E1(n). (i) ), and then use empirical mode decomposition to re-evaluate r1(t)+β1E1(n) (i) Decompose N times to obtain N first-order IMF components of the PPG signal. That is, the second-order IMF component of the original PPG signal, for the obtained N... The average value of the components is obtained Its expression is as follows:
[0073]
[0074] S4: To further understand the contribution of different level modes in the PPG signal to the original signal, the k-th order residual component r is calculated. k (t), whose expression is as follows:
[0075]
[0076] S5: Using the Empirical Mode Decomposition (EMD) algorithm to analyze r k (t)+β k n i After processing, the (k+1)th order IMF component of the original signal can be obtained as follows: For r k (t)+β k n i After decomposing N times and averaging, the final k+1 order IMF component is obtained. The expression is as follows:
[0077]
[0078] S6: Repeating steps S4 and S5 can gradually obtain the next-order IMF component. This iterative process will continue until the termination condition of the maximum number of iterations is met.
[0079] The preset condition is the maximum number of iterations. Each iteration generates a set of noisy signals. This invention sets the iteration range to 80-200, and then applies an empirical mode decomposition algorithm for repeated decomposition until the maximum number of iterations is reached. Users select the number of iterations according to different noise reduction depth requirements. Generally, more iterations may result in more refined signal decomposition, but also require more computational resources. Conversely, fewer iterations may lead to a coarser decomposition of signal features, but the computation speed is faster. Selecting an appropriate number of iterations usually requires specific experiments and evaluations to ensure that the signal noise reduction requirements are met.
[0080] The formula after decomposing the original function is as follows:
[0081]
[0082] In the above formula, R represents a series of IMF components. k (t) is the final remainder, which is the residual remaining after decomposition into all IMF components.
[0083] like Figure 4 The image shows the components of the PPG signal, as follows: Figure 5 The image shows the IMF components generated by Ceemdan decomposition of the PPG signal. Figure 4 and Figure 5 Perform subsequent calculations.
[0084] Step 3: Calculate the correlation coefficient of each intrinsic mode component (IMF). Based on the evaluation criteria of the correlation coefficient, evaluate the correlation between each IMF and the original signal, select the discrimination value, and classify them into correlated IMF and uncorrelated IMF based on the discrimination value.
[0085] The criteria for using the correlation coefficient for evaluation are as follows: when |r| < 0.3, it is uncorrelated; when 0.3 ≤ |r| < 0.5, it is poorly correlated; when 0.5 ≤ |r| < 0.8, it is significantly correlated; and when |r| ≥ 0.8, it is highly correlated. The distinguishing value for differentiating between correlated and uncorrelated IMF components is selected according to the evaluation criteria. In this embodiment, the distinguishing value is 0.3.
[0086] The formula for calculating the correlation coefficient r of each order of intrinsic mode component (IMF) is as follows:
[0087]
[0088] In the above formula, X(t) is the noisy PPG signal. The average value of the noisy PPG signal. Let be the mean of the i-th order IMF component.
[0089] The correlation coefficients of each IMF were calculated based on the formula shown in Table 1 below:
[0090] Table 1: Results of each IMF component
[0091]
[0092] For the data in Table 1, to distinguish between correlated and uncorrelated IMF components, a threshold value of 0.3 or higher was selected. This means that IMF6, IMF7, and IMF8 are retained as the relevant and valid components, while the remaining IMF1–5, IMF9–15, and RES components are classified as uncorrelated components in the pulse signal. Although the uncorrelated components mostly contain noise, they still retain valid signals. Therefore, directly reconstructing the PPG signal may result in the loss of some valid signals. Here, an improved wavelet thresholding method is used to remove noise components from the uncorrelated IMF components. Before using the improved wavelet thresholding for noise reduction, a suitable decomposition scale and wavelet basis need to be selected. Based on the correlation coefficient results, the correlation between each intrinsic mode component (IMF) and the original signal can be evaluated, and further verification will be provided through actual experiments. When processing PPG signals, noise usually exists in the high-frequency part, that is, in the uncorrelated IMF components after CEEMDAN decomposition. However, some effective signals still exist in the uncorrelated IMF components. If only the correlated components of the decomposed IMF are reconstructed, the effective information in some uncorrelated components will be lost. Therefore, in order to retain the effective information in the uncorrelated components, the integrated denoising algorithm of CEEMDAN combined with wavelet threshold proposed in this invention is used to further process the uncorrelated components.
[0093] Step 4: Perform wavelet decomposition on the uncorrelated intrinsic mode components (IMFs), set a wavelet threshold to remove noise from the uncorrelated intrinsic mode components (IMFs), and obtain the denoised uncorrelated intrinsic mode components.
[0094] The original signal is transformed into the wavelet domain for processing to obtain wavelet coefficients at different scales and frequencies, and simulation experiments are conducted to determine the threshold and the number of decomposition layers.
[0095] Currently, commonly used thresholding methods include Minimaxi, Heursure, Rigrsure, and Sqtolog thresholding. Through simulation experiments, the signal-to-noise ratio (SNR) of different decomposition levels under Minimaxi, Heursure, Rigrsure, and Sqtolog thresholding was analyzed, and the optimal decomposition level for the PPG signal was determined to be 3 levels. Comparing the SNR under Sym wavelet, db wavelet, and coif wavelet systems, the optimal wavelet basis for the PPG signal was determined to be db4. The analysis results are as follows: Figures 6-7 Based on the optimal threshold and the number of decomposition layers, either a soft thresholding or a hard thresholding function is used for denoising. Using a hard thresholding function helps to preserve the local features of the PPG signal. The denoising formula is as follows:
[0096]
[0097] While the soft thresholding function provides a smoother PPG signal than the hard thresholding function, it loses some detail. Its denoising formula is as follows:
[0098]
[0099] In the above formula, ω represents the wavelet coefficients, and δ... thr The threshold value is used.
[0100] In this embodiment, a hard thresholding function is selected for noise reduction.
[0101] Step 5: Reconstruct the signal to obtain the denoised signal. This completes the signal reconstruction after CEEMDAN decomposition, i.e., IMF combination. Correlation components with a correlation coefficient above 0.3 are directly linearly combined, and the residual RES is incorporated to obtain the signal.
[0102] The signal after wavelet thresholding denoising of the uncorrelated components is then reconstructed. This involves decomposing the original PPG signal into wavelet coefficients at multiple scales using wavelet transform, performing hard thresholding to reduce small-amplitude wavelet coefficients and remove noise components, and then using the remaining wavelet coefficients for inverse wavelet transform to restore the signal from the wavelet domain back to the original domain. The resulting reconstructed expression is:
[0103] The final formula for the reconstructed signal is as follows:
[0104]
[0105] like Figure 8 As shown, by combining the above formula, we obtain a schematic diagram of the PPG after denoising, and by combining the schematic diagram of the PPG before denoising, we obtain a comparison diagram before and after denoising.
[0106] The denoising method of this invention is compared with traditional methods. A noise signal is selected, and considering the characteristics of the PPG signal itself, 10dB of random white noise is added to the preprocessed noiseless signal. This method is compared with traditional wavelet threshold denoising, CEEMDAN denoising, and empirical mode decomposition algorithm combined with improved wavelet threshold denoising. The signal-to-noise ratio and mean square error are calculated, and the results are shown in Table 2 below.
[0107] Table 2 Comparison of Noise Reduction Methods
[0108]
[0109] Table 2 shows the specific data comparing other methods with the method of this invention. It is clear that compared to traditional single-method denoising and basic EMD combined algorithm denoising, the CEEMDAN combined with improved wavelet threshold denoising method presented in this paper has a higher signal-to-noise ratio and a smaller mean square error, demonstrating excellent denoising performance. Using only wavelet denoising or the CEEMDAN algorithm for PPG signal denoising yields unsatisfactory results and easily causes signal distortion after denoising. This invention employs a method combining CEEMDAN and wavelet thresholding. Experimental results show that the signal-to-noise ratio and mean square error are superior to other single algorithms and some combined algorithms. This method preserves the non-stationary characteristics of the original PPG signal to the greatest extent. For the IMF components obtained from CEEMDAN decomposition, this invention does not directly discard the uncorrelated components but uses a wavelet transform-based denoising method to retain the effective components in the uncorrelated components.
[0110] Therefore, this invention employs a PPG signal denoising method based on CEMDAN combined with wavelet thresholding, which preserves the non-stationary characteristics of the original PPG signal to the maximum extent and retains as much effective information as possible. For the IMF components obtained from CEMDAN decomposition, this invention does not directly discard the uncorrelated IMF components, but instead uses a wavelet transform-based denoising method to retain the effective components within the uncorrelated IMF components.
[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.
Claims
1. A PPG signal denoising method based on CEMDAN combined with wavelet thresholding, characterized in that: Includes the following steps: Step 1: Set up the detection platform and collect photoplethysmography (PPG) signals; Step 2: Use the CEEMDAN algorithm to decompose the PPG signal and obtain the Intrinsic Mode Components (IMFs) of each order of the PPG signal; Step 3: Calculate the correlation coefficient r of each intrinsic mode component (IMF). Based on the evaluation criteria of the correlation coefficient, evaluate the correlation between each IMF and the original signal, select the discrimination value, and classify them into correlated IMF and uncorrelated IMF based on the discrimination value. Step 4: Perform wavelet decomposition on the uncorrelated intrinsic mode components (IMFs), set a wavelet threshold to remove noise from the uncorrelated intrinsic mode components (IMFs), and obtain the denoised uncorrelated intrinsic mode components. Step 5: Reconstruct the signal to obtain the denoised signal.
2. The PPG signal denoising method based on CEMDAN combined with wavelet thresholding according to claim 1, characterized in that: In step one, the detection platform includes seven modules: a pulse acquisition module, a preamplifier module, a 50Hz notch filter module, a 10Hz low-pass filter module, a main amplifier module, an AD conversion module, and an STM32 main control module. The detection platform records data at a sampling frequency of 200Hz.
3. The PPG signal denoising method based on CEMDAN combined with wavelet thresholding according to claim 2, characterized in that: In step two, the specific steps for decomposing the PPG signal using the CEEMDAN algorithm are as follows: In the CEEMDAN process, β is defined. i Let n be the i-th noise figure. i It is Gaussian white noise with a mean of 0 and a variance of 1; S1: The original PPG signal is superimposed with Gaussian white noise to form the signal to be decomposed, as shown in the following formula: x (i) =x+β0n i (1) In the above formula, x is the original PPG signal, and then x (i) First-order IMF components were obtained by performing Empirical Mode Decomposition (EMD). The decomposition expression of the remaining component r1(t) is as follows: In the above formula, This represents the first intrinsic mode component after EMD decomposition of the original PPG signal and Gaussian white noise. The final first-order intrinsic mode component is obtained by repeating EMD decomposition on the original signal N times and taking the average. The expression is as follows: S2: Calculate the first-order remainder r1(t), where r1(t) is the remainder after removing the first-order remainder from the original signal. The remaining part is expressed as follows: S3: Obtain the second-order intrinsic mode components and add noise β1n to the remainder term r1(t). i The signal to be decomposed is obtained as r1(t) + β1E1(n). (i) ), and then use empirical mode decomposition to re-evaluate r1(t)+β1E1(n) (i) Decompose N times to obtain N first-order IMF components of the PPG signal. That is, the second-order IMF component of the original PPG signal, for the obtained N... The average value of the components is obtained Its expression is as follows: S4: Calculate the residual component r of order k. k (t), whose expression is as follows: S5: r is analyzed through empirical mode decomposition. k (t)+β k n i After processing, the (k+1)th order IMF component of the original signal is obtained as follows: For r k (t)+β k n i After decomposing N times and averaging, the final k+1 order IMF component is obtained. The expression is as follows: S6: Repeat steps S4 and S5 until the next-order IMF component is obtained. This iterative process will continue until the termination condition of the maximum number of iterations is met. The formula after decomposing the original function is as follows: In the above formula, R represents a series of IMF components. k (t) is the final remainder.
4. The PPG signal denoising method based on CEMDAN combined with wavelet thresholding according to claim 3, characterized in that: In step three, the criteria for evaluation using the correlation coefficient are as follows: When |r| < 0.3, it is uncorrelated; when 0.3 ≤ |r| < 0.5, it is poorly correlated; when 0.5 ≤ |r| < 0.8, it is significantly correlated; when |r| ≥ 0.8, it is highly correlated. The distinguishing value between correlated and uncorrelated IMF components should be set according to the evaluation criteria.
5. The PPG signal denoising method based on CEMDAN combined with wavelet thresholding according to claim 4, characterized in that: In step three, the formula for calculating the correlation coefficient of each order of intrinsic mode component (IMF) is as follows: In the above formula, X(t) is the noisy PPG signal. The average value of the noisy PPG signal. Let be the mean of the i-th order IMF component.
6. The PPG signal denoising method based on CEMDAN combined with wavelet thresholding according to claim 5, characterized in that: In step four, the specific process of setting a wavelet threshold to remove noise from the uncorrelated intrinsic mode components (IMF) is as follows: The original signal is transformed into the wavelet domain for processing to obtain wavelet coefficients at different scales and frequencies. Simulation experiments are conducted to determine the wavelet basis and the number of decomposition layers. For PPG signals, the optimal number of decomposition layers is set to 3, and the optimal wavelet basis is set to db4. Based on the wavelet basis and the number of decomposition layers, soft thresholding or hard thresholding functions are used for denoising.
7. A PPG signal denoising method based on CEMDAN combined wavelet thresholding according to claim 6, characterized in that: In step five, the formula for reconstructing the signal is as follows: In the above formula, It is a combination of relevant intrinsic modal components and residuals. It is a combination of unrelated intrinsic mode components after wavelet thresholding for denoising.