A signal denoising method based on self-supervised learning

Abstract

The present invention provides a signal denoising method based on self-supervised learning, which relates to the field of signal processing, including signal frequency decomposition: using a balanced multi-level signal decomposition method BHD to decompose signal data to obtain fine-grained frequency coefficients of the signal; self-supervised representation learning: using an automatic labeling strategy to label the frequency coefficients, constructing a neural network to perform supervised representation learning on the obtained labeled data, and obtaining an embedded representation of each frequency coefficient; selective signal reconstruction, according to the high and low noise frequency in the actual scene, the embedded representation of the obtained frequency coefficients is divided into a noise group and a denoising group, and the denoising group frequency coefficients are used to reconstruct the signal, and the reconstructed signal obtained is the denoising result of the corresponding signal. The present invention does not require pure signal data in the denoising process, does not rely on human experience, and is independent of specific scenes. It has high versatility while effectively denoising.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to a signal denoising method based on self-supervisory learning. Background Art

[0002] With the continuous development of modern intelligent industry, various sensors are widely used in various industries, and a large amount of sensor data is generated. For example, biomedical signals such as electrocardiogram (ECG) collected by wearable devices can be used for intelligent medical and health monitoring; microphones receive human voice as voice signals in communication services; sensors are used to monitor environmental pollution levels to understand the long-term physical and chemical performance of the ecosystem. The deployment of sensors has made a significant contribution to the development of intelligent perception.

[0003] The signals collected by sensors are typical time series data. However, in most practical situations, the collected signals are often contaminated by noise caused by various interference factors (e.g., low-quality network transmission and measurement errors). Analyzing these noisy signals can lead to inaccurate results, such as misdiagnosis of heart disease, speech recognition errors, and inaccurate assessment of pollution. Therefore, signal denoising is the primary task to improve the performance of signal analysis.

[0004] Typically, in most denoising methods, the original signal will be transformed into the frequency domain or decomposed into a series of coefficients. Traditional methods have limited generalization performance. For example, spectral subtraction may lead to negative amplitude spectrum problems. Deep learning methods are applied to a variety of fields due to their significant expressive learning capabilities, and deep learning methods are also used to solve denoising problems. In deep learning methods, supervised learning models usually achieve higher performance due to strong supervision during the model training phase. However, during training, supervised learning methods require clean signals without noise as supervisory information. Manually processing signals to obtain clean signals requires a lot of manpower, which is not feasible in practical applications. In order to avoid the reliance on clean signals during the training phase, unsupervised methods are used for signal denoising. Unsupervised methods usually set a threshold to filter out frequencies that are considered noise frequencies by human experience. The setting of the threshold usually relies on human experience. Although some methods can use clean signals to improve the threshold determination method, this operation converts the frequency selection process back to a supervised learning problem and cannot completely get rid of the reliance on clean signals. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a signal denoising method based on self-supervised learning. A signal denoising method based on self-supervised learning comprises the following steps:

[0006] Step 1: Use the balanced multi-level signal decomposition method BHD to perform frequency decomposition on the signal data to obtain fine-grained frequency coefficients of the signal;

[0007] First, we need to set the decomposition level m for the balanced multi-level signal method BHD according to the actual decomposition effect, and use discrete wavelet transform to decompose the signal data at each level. The formula of discrete wavelet transform is as follows:

[0008]

[0009] Where t represents time, x(t) represents the decomposed signal, α and τ represent the scale parameter and the conversion parameter respectively, and ψ(·) represents the wavelet function. The high-frequency coefficients and low-frequency coefficients obtained by discrete wavelet transform are decomposed iteratively. The decomposition level m of the balanced multi-level signal decomposition method BHD is the number of iterations.

[0010] Step 2: Use the automatic labeling strategy to label the fine-grained frequency coefficients of the obtained signal, build a neural network to perform supervised representation learning on the obtained labeled data, and obtain the embedded representation of each frequency coefficient;

[0011] Step 2.1: Label each pair of frequency coefficients based on their proximity and waveform similarity;

[0012] Step 2.1.1: The index of frequency coefficient A in the result list returned by the balanced multi-level decomposition signal decomposition method BHD is i, and the index of frequency coefficient B in the result list returned by BHD is j. Adjacent frequency coefficients are defined as |ij|=1, that is, the two frequency coefficients are at the same level of the balanced multi-level signal decomposition method BHD decomposition tree and are adjacent;

[0013] Step 2.1.2: The waveform similarity is measured using the dynamic time warping (DTW) distance. The dynamic time warping (DTW) algorithm uses a dynamic programming method to find the best alignment path between two time series elements. The dynamic time warping (DTW) distance is the sum of the Euclidean distances between the aligned elements on the best alignment path. Given two time series A with dimensions m and n, A = {a1, a2, ...a i , ...a n} and B = {b1, b2, ... b i , ...b m}, calculate the distance matrix D between A and B, the element D in D i，j represents the Euclidean distance between two elements in A and B, D i，j The calculation method is as follows:

[0014] D i，j =||a i -b j ||

[0015] After obtaining the distance matrix D, the cost matrix R is constructed using the dynamic programming algorithm. The elements R in R i，j Indicates that from D 1，1 To D i，j The minimum distance; R i，j The calculation method is as follows:

[0016] R i，j =D i，j +min{R i-1，j , R i-1，j-1 , R i，j-1}

[0017] Where R 0，0 =0, R i，0 =∞,R 0，j =∞. After obtaining the cost matrix R, find the cost matrix R from D 1，1 To D m，n The minimum cumulative distance path is W = {ω1, ω2, ...ω k ,...ω p} represents the path, the path length is p, where ω k = (i, j) represents the index of the corresponding element in the distance matrix D; Finally, the dynamic time warping DTW distance between two time series is R m，n , calculated as follows:

[0018]

[0019] Step 2.1.3: After obtaining the adjacency of the frequency coefficients according to step 2.1.1 and the similarity of the frequency coefficients according to step 2.1.2, label them according to two rules:

[0020] Rule a: The smaller the DTW distance, the higher the similarity of a pair of frequency coefficients. It is determined whether the distance between a pair of frequency coefficients is less than the threshold ε.

[0021] Rule b: Determine whether a pair of frequency coefficients are adjacent;

[0022] If a pair of frequency coefficients (c i ,c j ) If both of the above rules are met, their labels are set to 1, otherwise their labels are set to 0. The formula is as follows:

[0023]

[0024] Step 2.2: Construct a two-channel convolutional neural network, take a pair of frequency coefficients as the input data of the network, and use the label of the pair of data as supervision information, and use the classification task to learn high-quality embedding representations of all frequency coefficients in a supervised manner;

[0025] In order to extract the deep features of frequency coefficients, a two-channel convolutional neural network is designed; the network accepts a frequency coefficient pair as input, and each coefficient is fed into a separate channel; each channel consists of three convolution modules CM and a one-dimensional convolution layer; each module contains three one-dimensional convolution layers and one maximum pooling layer; a concatenation layer is used to connect the embedded representations of the two input coefficients; finally, a fully connected layer with soft-max as the activation function outputs the classification result;

[0026] Step 3: According to the noise frequency in the actual scenario, the embedded representation of the obtained frequency coefficients is divided into a noise group and a denoising group, and the signal is reconstructed using the denoising group frequency coefficients. The reconstructed signal is the denoising result of the corresponding signal.

[0027] The deep feature embedding representation generated by the dual-channel convolutional neural network is used to determine which frequency coefficients are involved in the reconstruction of the signal; the clustering method is used to divide all the frequency coefficients of the signal into two clusters based on the potential similarity of the embedding representation; according to the noise frequency in the actual scene, the frequency coefficients in the cluster with non-noise frequency at the cluster center in the clustering result are used to reconstruct the signal. The reconstructed signal is the denoising result of the corresponding signal.

[0028] The beneficial technical effects of the present invention are:

[0029] The present invention provides a signal denoising method based on self-supervision, including a balanced multi-level signal decomposition method, referred to as BHD, so as to obtain the fine-grained frequency coefficients of the signal, label the frequency coefficients using the proposed automatic labeling strategy, and perform supervised frequency coefficient embedding representation learning through a neural network, which is used as the basis for selective reconstruction of the signal, gets rid of the dependence of signal denoising on pure signals, does not require manual labeling, and improves work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of a signal denoising method based on self-supervised learning of the present invention;

[0031] Figure 2 It is a schematic diagram of the balanced multi-level signal decomposition method BHD in the method of the present invention;

[0032] Figure 3 It is a structural diagram of a dual-channel neural network model in the method of the present invention. DETAILED DESCRIPTION

[0033] The present invention is further described below in conjunction with the accompanying drawings and embodiments; the present invention provides a deep learning signal denoising method that does not require setting a threshold based on human experience and does not rely on pure signals as supervisory information;

[0034] Deep learning methods are widely used in various fields due to their powerful representation learning capabilities. When faced with the problem of signal denoising, traditional deep learning methods require a large amount of pure signals as supervisory information for model learning. However, in real scenarios, a large amount of pure signals are difficult or even impossible to obtain. In view of this situation, the present invention solves the problem of signal denoising without pure signal supervision.

[0035] like Figure 1 As shown, a signal denoising method based on self-supervised learning specifically includes the following steps:

[0036] Step 1: Use the balanced multi-level signal decomposition method BHD to perform frequency decomposition on the signal data to obtain fine-grained frequency coefficients of the signal;

[0037] The balanced multi-level signal decomposition method BHD is used to decompose the signal. Discrete wavelet transform is used for decomposition at each level. The high-frequency coefficients and low-frequency coefficients obtained by each decomposition are iteratively decomposed to obtain the fine-grained frequency coefficients of the signal.

[0038] First, we need to set the decomposition level m for the balanced multi-level signal method BHD according to the actual decomposition effect, and use discrete wavelet transform to decompose the signal data at each level. The formula of discrete wavelet transform is as follows:

[0039]

[0040] Wherein, t represents time, x(t) represents the decomposed signal, α and τ represent the scale parameter and the conversion parameter respectively, and ψ(·) represents the wavelet function; the high-frequency coefficients and low-frequency coefficients obtained by discrete wavelet transform are iteratively decomposed, and the decomposition level m of the balanced multi-level signal decomposition method BHD is the number of iterations; the high-frequency coefficients and low-frequency coefficients obtained by discrete wavelet transform are iteratively decomposed, and the decomposition level m of the balanced multi-level signal decomposition method BHD is the number of iterations. The schematic diagram of the balanced multi-level signal decomposition method BHD is shown in Figure 2 As shown, Figure 2 The decomposition level of BHD is level 3.

[0041] A description of the balanced multi-level signal decomposition method is given below in pseudo-code form:

[0042]

[0043]

[0044] The BHD algorithm accepts the original signal s and the decomposition level m as input. First, an empty list l is initialized to save the intermediate wavelet coefficients (line 1). The original signal s is added to list l as the first element in the list (line 2). For each decomposition level (line 3), BHD obtains the n wavelet coefficients to be transformed in that level (lines 4 and 5), that is, all leaf nodes of the current multi-level decomposition tree, and performs a discrete wavelet transform on each coefficient (line 6). The obtained high-frequency coefficients ca and low-frequency coefficients cd are added to list 1 for the next level of decomposition (lines 7-9). Finally, the leaf elements of the m-level decomposition tree are taken as the decomposition results and returned as the results (lines 10 and 11).

[0045] Step 2: Use the automatic labeling strategy to label the fine-grained frequency coefficients of the obtained signal, build a neural network to perform supervised representation learning on the obtained labeled data, and obtain the embedded representation of each frequency coefficient;

[0046] Step 2.1: Label each pair of frequency coefficients based on their proximity and waveform similarity;

[0047] Step 2.1.1: The index of frequency coefficient A in the result list returned by the balanced multi-level decomposition signal decomposition method BHD is i, and the index of frequency coefficient B in the result list returned by BHD is j. Adjacent frequency coefficients are defined as |ij|=1, that is, the two frequency coefficients are at the same level of the balanced multi-level signal decomposition method BHD decomposition tree and are adjacent;

[0048] Step 2.1.2: The waveform similarity is measured using the dynamic time warping (DTW) distance. The dynamic time warping (DTW) algorithm uses a dynamic programming method to find the best alignment path between two time series elements. The dynamic time warping (DTW) distance is the sum of the Euclidean distances between the aligned elements on the best alignment path. Given two time series A with dimensions m and n, A = {a1, a2, ...a i , ...a n} and B = {b1, b2, ... b i , ...b m}, calculate the distance matrix D between A and B, the element D in D i，j represents the Euclidean distance between two elements in A and B, D i，j The calculation method is as follows:

[0049] D i，j =||a i -b j ||

[0050] After obtaining the distance matrix D, the cost matrix R is constructed using the dynamic programming algorithm. The elements R in R i，j Indicates that from D1，1 To D i，j The minimum distance; R i，j The calculation method is as follows:

[0051] R i，j =D i，j +min{R i-1，j , R i-1，j-1 , R i，j-1}

[0052] Where R 0，0 =0, R i，0 =∞,R 0，j =∞. After obtaining the cost matrix R, find the cost matrix R from D 1，1 To D m，n The minimum cumulative distance path is W = {ω1, ω2, ...ω k ,...ω p} represents the path, the path length is p, where ω k = (i, j) represents the index of the corresponding element in the distance matrix D; Finally, the dynamic time warping DTW distance between two time series is R m，n , calculated as follows:

[0053]

[0054] Step 2.1.3: After obtaining the adjacency of the frequency coefficients according to step 2.1.1 and the similarity of the frequency coefficients according to step 2.1.2, label them according to two rules:

[0055] Rule a: The smaller the DTW distance, the higher the similarity of a pair of frequency coefficients. It is determined whether the distance between a pair of frequency coefficients is less than the threshold ε.

[0056] Rule b: Determine whether a pair of frequency coefficients are adjacent;

[0057] If a pair of frequency coefficients (c i , c j ) If both of the above rules are met, their labels are set to 1, otherwise their labels are set to 0. The formula is as follows:

[0058]

[0059] Step 2.2: Construct a two-channel convolutional neural network, take a pair of frequency coefficients as the input data of the network, and use the label of the pair of data as supervision information, and use the classification task to learn high-quality embedding representations of all frequency coefficients in a supervised manner;

[0060] In order to extract the deep features of the frequency coefficients, a dual-channel convolutional neural network is designed; the network structure is as follows Figure 3 As shown in the figure. The network accepts a frequency coefficient pair as input, and each coefficient is fed into a separate channel; each channel consists of three convolution modules CM and a one-dimensional convolution layer; each module contains three one-dimensional convolution layers and a maximum pooling layer; a concatenation layer is used to connect the embedded representations of the two input coefficients; finally, a fully connected layer with soft-max as the activation function outputs the classification result;

[0061] After supervised training of the network with labeled samples obtained in step 2.1, high-quality embedding representations of frequency coefficients can be obtained through separate channels of the feature extraction part of the network.

[0062] Step 3: According to the noise frequency in the actual scenario, the embedded representation of the obtained frequency coefficients is divided into a noise group and a denoising group, and the signal is reconstructed using the denoising group frequency coefficients. The reconstructed signal is the denoising result of the corresponding signal.

[0063] The deep feature embedding representation generated by the dual-channel convolutional neural network is used to determine which frequency coefficients participate in the reconstruction of the signal; clustering methods, such as k-means, are used to divide all the frequency coefficients of the signal into two clusters based on the potential similarity of the embedding representation; according to the noise frequency in the actual scenario, the frequency coefficients in the cluster with non-noise frequency at the cluster center in the clustering result are used to reconstruct the signal. The reconstructed signal obtained is the denoising result of the corresponding signal. In practical applications, the frequency coefficient of which cluster participates in the reconstruction can be determined based on the noise frequency level. In most scenarios, the frequency of the noise is relatively high, so in this case, the cluster with low-frequency coefficients at the cluster center frequency is used to reconstruct the signal, and the reconstruction result is the corresponding denoised signal.

Claims

1. A signal denoising method based on self-supervised learning, characterized in that: The specific steps include: Step 1: Use the balanced multi-level signal decomposition method BHD to perform frequency decomposition on the signal data to obtain fine-grained frequency coefficients of the signal; Step 1 is as follows: First, we need to set the decomposition level m for the balanced multi-level signal method BHD according to the actual decomposition effect, and use discrete wavelet transform to decompose the signal data at each level. The formula of discrete wavelet transform is as follows: Where t represents time, x(t) represents the decomposed signal, α and τ represent the scale parameter and the conversion parameter respectively, and ψ(·) represents the wavelet function. The high-frequency coefficients and low-frequency coefficients obtained by discrete wavelet transform are decomposed iteratively. The decomposition level m of the balanced multi-level signal decomposition method BHD is the number of iterations. Step 2: Use the automatic labeling strategy to label the fine-grained frequency coefficients of the obtained signal, build a neural network to perform supervised representation learning on the obtained labeled data, and obtain the embedded representation of each frequency coefficient; Step 2 is as follows: Step 2.1: Label each pair of frequency coefficients based on their proximity and waveform similarity; Step 2.2: Construct a two-channel convolutional neural network, take a pair of frequency coefficients as the input data of the network, and use the label of the pair of data as supervision information, and use the classification task to learn high-quality embedding representations of all frequency coefficients in a supervised manner; Step 3: According to the noise frequency in the actual scenario, the embedded representation of the obtained frequency coefficients is divided into a noise group and a denoising group, and the signal is reconstructed using the denoising group frequency coefficients. The reconstructed signal is the denoising result of the corresponding signal.

2. The signal denoising method based on self-supervised learning according to claim 1, characterized in that: Step 2.1 is as follows: Step 2.1.1: The index of frequency coefficient A in the result list returned by the balanced multi-level decomposition signal decomposition method BHD is i, and the index of frequency coefficient B in the result list returned by BHD is j. Adjacent frequency coefficients are defined as |ij|=1, that is, the two frequency coefficients are at the same level of the balanced multi-level signal decomposition method BHD decomposition tree and are adjacent; Step 2.1.2: The waveform similarity is measured using the dynamic time warping (DTW) distance. The dynamic time warping (DTW) algorithm uses a dynamic programming method to find the best alignment path between two time series elements. The dynamic time warping (DTW) distance is the sum of the Euclidean distances between the aligned elements on the best alignment path. Given two time series A with dimensions m and n, respectively, A = {a1, a2, … a i ,…a n } and B={b1,b2,…b i ,…b m }, calculate the distance matrix D between A and B, the element D in D i,j represents the Euclidean distance between two elements in A and B, D i,j The calculation method is as follows: D i,j =||a i -b j || After obtaining the distance matrix D, the cost matrix R is constructed using the dynamic programming algorithm. The elements R in R i,j Indicates that from D 1,1 To D i,j The minimum distance; R i,j The calculation method is as follows: R i,j =D i,j +min{R i-1,j ,R i-1,j-1 ,R i,j-1 } Where R 0,0 =0,R i,0 =∞,R 0,j =∞; After obtaining the cost matrix R, find the cost matrix R from D 1,1 To D m,n The minimum cumulative distance path is W = {ω1, ω2, …ω k ,…ω p } represents the path, the path length is p, where ω k =(i,j) represents the index of the corresponding element in the distance matrix D; finally, the dynamic time warping DTW distance between two time series is R m,n , calculated as follows: Step 2.1.3: After obtaining the adjacency of the frequency coefficients according to step 2.1.1 and the similarity of the frequency coefficients according to step 2.1.2, label them according to the two rules.

3. The signal denoising method based on self-supervised learning according to claim 2, characterized in that: The two rules described in step 2.1.3 are specifically: Rule a: The smaller the DTW distance, the higher the similarity of a pair of frequency coefficients. It is determined whether the distance between a pair of frequency coefficients is less than the threshold ε. Rule b: Determine whether a pair of frequency coefficients are adjacent; If a pair of frequency coefficients (c i ,c j ) If both of the above rules are met, their labels are set to 1, otherwise their labels are set to 0. The formula is as follows:

4. The signal denoising method based on self-supervised learning according to claim 1, characterized in that: Step 2.2 is as follows: In order to extract the deep features of frequency coefficients, a two-channel convolutional neural network is designed; the network accepts a frequency coefficient pair as input, and each coefficient is fed into a separate channel; each channel consists of three convolution modules CM and a one-dimensional convolution layer; each module contains three one-dimensional convolution layers and one maximum pooling layer; A concatenation layer is used to connect the embedded representations of the two input coefficients; finally, a fully connected layer with soft-max as the activation function outputs the classification result.

5. The signal denoising method based on self-supervised learning according to claim 1, characterized in that: Step 3 is as follows: The deep feature embedding representation generated by the dual-channel convolutional neural network is used to determine which frequency coefficients are involved in the reconstruction of the signal; the clustering method is used to divide all the frequency coefficients of the signal into two clusters according to the potential similarity of the embedding representation; according to the high and low noise frequency in the actual scenario, the frequency coefficients in the cluster of non-noise frequency at the cluster center in the clustering result are used to reconstruct the signal; the reconstructed signal obtained is the denoising result of the corresponding signal.

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