Surface electromyogram signal decomposition method based on gradient convolution kernel compensation

Abstract

The invention discloses a surface electromyogram signal decomposition method based on gradient convolution kernel compensation, which belongs to the technical field of biological signal extraction, and comprises the following steps: collecting multi-channel surface electromyogram signals; expanding the surface electromyogram signal according to a preset expansion factor to obtain an expanded surface electromyogram signal; whitening the expanded surface electromyogram signal to obtain a whitened surface electromyogram signal; calculating a cross-correlation matrix, and initializing an activity index; initializing a cross-correlation vector according to the activity index; obtaining a preset gradient function and a learning rate, and carrying out iterative updating on the cross-correlation vector; calculating an issuing time sequence of the motion unit according to the updated cross-correlation vector and the whitened surface electromyogram signal; taking the obtained issuing time sequence as a reference signal, and performing error correction on the reference signal by using a correlation constraint FastICA to obtain an optimized motion unit issuing time sequence; and repeatedly decomposing until a new motion unit distribution time sequence cannot be decomposed. According to the method, the surface electromyogram signal decomposition precision can be improved.

Description

Technical Field

[0001] The present invention belongs to the field of biological signal processing, and relates to a method for decomposing electromyography signals. Specifically, it particularly relates to a method for decomposing surface electromyography signals based on gradient convolution kernel compensation. Background Art

[0002] Electromyography signals are relatively ideal physiological electrical signals that can be used to extract motion information in practical applications. These information can be used to study the characteristics of human muscle nerve coding, including the type of movement, the health of muscles, etc. In the past few decades, electromyography signals have been widely used in various scientific research in the field of medical health.

[0003] The motion information carried by electromyography signals can be extracted through the decomposition of electromyography signals. According to the generation principle of electromyography signals, electromyography signals can be decomposed into the action potential of motor units (Motor Unit Action Potential, MUAP) and the firing time series of motor units (Motor Unit, MU). Among them, the research on MUAP can lay the foundation for clinical disease diagnosis based on morphological biometric characteristics, and the research on the MU firing time series can provide important reference basis for the diagnosis of central nervous system dysfunction.

[0004] Surface electromyography signals are collected by recording electrodes placed on the skin surface. The collection process is simple and convenient and is non-invasive to the body. Surface electromyography signals can usually be regarded as a convolutional mixture model, and blind source separation methods such as gradient convolution kernel compensation and FastICA are often used for decomposition. However, due to the easy occurrence of poor contact between the collection electrode and the skin, there is noise interference in the collected electromyography signals, thus affecting the accuracy of the decomposition results. Summary of the Invention

[0005] In view of the deficiencies of the existing technology, the present invention provides a method for decomposing surface electromyography signals based on gradient convolution kernel compensation. The present invention is based on gradient convolution kernel compensation and related constrained FastICA, and can reduce the interference of factors such as noise when decomposing electromyography signals, and improve the accuracy of the decomposition results of electromyography signals.

[0006] The technical means adopted by the present invention are as follows:

[0007] A method for decomposing surface electromyography signals based on gradient convolution kernel compensation, comprising the following steps:

[0008] S1. Collect surface electromyography signals of multiple channels;

[0009] S2. Expand the surface electromyography signals according to a preset expansion factor to obtain the expanded surface electromyography signals;

[0010] S3. Calculate the whitening matrix based on the extended surface electromyogram signal, and perform whitening processing on the extended surface electromyogram signal based on the whitening matrix to obtain the whitened surface electromyogram signal;

[0011] S4. Calculate the cross-correlation matrix according to the whitened surface electromyogram signal, and initialize the activity index;

[0012] S5. Initialize the cross-correlation vector according to the activity index;

[0013] S6. Obtain the preset gradient function and learning rate, and perform iterative update on the cross-correlation vector;

[0014] S7. Calculate the firing time series of the motor unit according to the updated cross-correlation vector and the whitened surface electromyogram signal;

[0015] S8. Use the obtained firing time series as the reference signal, and correct the reference signal using the correlated constrained FastICA to obtain the optimized firing time series of the motor unit;

[0016] S9. Repeat S5 to S8 until no new firing time series of the motor unit can be decomposed.

[0017] Furthermore, the collected multi-channel surface electromyogram signal can be expressed as:

[0018] x = [x(1), x(2), x(3), …, x(n), …]

[0019] where x(n) = [x 1 (n), x 2 (n), …, x M (n)] T represents the surface electromyogram signal collected at the nth sampling moment, x i (n) is the component on the ith channel, and M represents the number of channels of the surface electromyogram signal.

[0020] Furthermore, the extended surface electromyogram signal is:

[0021]

[0022] where represents the surface electromyogram signal at the nth sampling moment after extension, d is the preset extension factor, the number of channels before extension is M, and the number of channels after extension is M(d + 1).

[0023] Furthermore, performing whitening processing on the extended surface electromyogram signal based on the whitening matrix includes:

[0024] According to the extended surface electromyogram signal Calculate the covariance matrix, and calculate the eigenvalues and eigenvectors of the covariance matrix;

[0025] Arrange the eigenvalues in descending order to form a diagonal matrix D, and form an eigenmatrix E by arranging the eigenvectors corresponding to the eigenvalues in order. Then the whitening matrix Q = sqrt(D) / E T , where sqrt() represents calculating the square root, and E T represents the transpose matrix of matrix E;

[0026] Apply the whitening matrix Q to the extended surface electromyogram signal to obtain the whitened surface electromyogram signal

[0027]

[0028] Furthermore, calculate the cross-correlation matrix based on the whitened surface electromyogram signal and initialize the activity index, including:

[0029] Based on the whitened surface electromyogram signal Calculate the cross-correlation matrix according to the following formula:

[0030]

[0031] where E() represents the mathematical expectation;

[0032] Initialize the activity index as:

[0033] γ = {γ(n); n = 1, 2, 3, …}

[0034] where

[0035] Furthermore, initialize the cross-correlation vector according to the activity index, including:

[0036] n 0 = max arg n (γ(n))

[0037] γ(n 0 ) = 0

[0038]

[0039] where γ(n) represents the activity index corresponding to the nth sampling moment, and n 0 represents the sampling moment corresponding to the maximum value of the activity index, and γ(n 0 ) = 0 means ensuring that the cross-correlation vector is initialized to different values repeatedly, represents the value of the whitened surface electromyogram signal at the n 0 moment, Represents the cross - correlation vector.

[0040] Furthermore, the iterative formula of the cross - correlation vector is:

[0041]

[0042] where η represents the learning rate, represents the gradient function, and represents the firing time series of the j - th motor unit.

[0043] Furthermore, according to the gradient convolution kernel compensation algorithm, the firing time series of the j - th motor unit is:

[0044]

[0045] where, represents the cross - correlation vector, represents the correlation matrix, represents the whitened surface electromyogram signal.

[0046] Furthermore, taking the obtained firing time series as the reference signal, using the correlation - constrained FastICA to correct the reference signal, the optimized firing time series of the motor unit is obtained, including:

[0047] Taking the obtained firing time series of the motor unit as the reference signal r and inputting it into the correlation - constrained FastICA to construct the optimization problem:

[0048]

[0049] where G is a non - polynomial function, taking G = logcosh(u), is a penalty term, and the penalty weight μ is a positive constant;

[0050] Using the Newton method to solve the optimization problem, the iterative formula of the decomposition coefficient vector w can be obtained:

[0051]

[0052] where,

[0053] Calculating the optimized firing time series of the motor unit according to the decomposition coefficient vector is:

[0054]

[0055] where, represents the whitened surface electromyogram signal.

[0056] Compared with the prior art, the present invention has the following advantages:

[0057] A method for decomposing surface electromyogram signals based on gradient convolution kernel compensation provided by the present invention can improve the accuracy of surface electromyogram signal decomposition, and can also maintain a high decomposition accuracy when the excitation level is increased. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0059] Figure 1 It is a flowchart of a method for decomposing surface electromyogram signals based on gradient convolution kernel compensation in an embodiment of the present invention.

[0060] Figure 2 It is a decomposition result diagram of the simulated surface electromyogram signal in Embodiment 1 of the present invention.

[0061] Figure 3 It is a decomposition result diagram of the simulated surface electromyogram signal in Embodiment 2 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0063] As Figure 1 shown, the present invention provides a method for decomposing surface electromyogram signals based on gradient convolution kernel compensation, including the following steps:

[0064] S1. Collect surface electromyogram signals of multiple channels.

[0065] The collected multi-channel surface electromyogram signals can be expressed as:

[0066] x = [x(1), x(2), x(3), …, x(n), …]

[0067] where x(n) = [x 1 (n), x 2 (n), …, x M (n)]T , where \(M\) represents the number of channels of the surface electromyogram signal. \(x(n)\) represents the surface electromyogram signal collected at the \(n\)th sampling moment, where \(x\) i (n) is the component on the \(i\)th channel.

[0068] S2. Expand the surface electromyogram signal according to a preset expansion factor to obtain the expanded surface electromyogram signal.

[0069] If the collected surface electromyogram signal is expanded based on a preset expansion factor \(d\), the expanded surface electromyogram signal is expressed as:

[0070]

[0071] where:

[0072]

[0073] represents the surface electromyogram signal at the \(n\)th sampling moment after expansion. The number of channels before expansion is \(M\), and the number of channels after expansion is \(M(d + 1)\).

[0074] S3. Calculate the whitening matrix based on the expanded surface electromyogram signal, and perform whitening processing on the expanded surface electromyogram signal based on the whitening matrix to obtain the whitened surface electromyogram signal.

[0075] According to the expanded surface electromyogram signal calculate the covariance matrix, and calculate the eigenvalues and eigenvectors of the covariance matrix; arrange the eigenvalues from largest to smallest to form a diagonal matrix \(D\), and form an eigenmatrix \(E\) by arranging the eigenvectors corresponding to the eigenvalues in order. Then the whitening matrix \(Q=\sqrt{D} / E\) T , where \(\sqrt{()}\) represents calculating the square root, and \(E\) T represents the transpose matrix of matrix \(E\); apply the whitening matrix \(Q\) to the expanded surface electromyogram signal to obtain the whitened surface electromyogram signal

[0076] S4. Calculate the cross-correlation matrix based on the whitened surface electromyogram signal and initialize the activity index.

[0077] Based on the whitened surface electromyogram signal, calculate the cross-correlation matrix: and initialize the activity index as: \(\gamma=\{\gamma(n);n = 1,2,3,\cdots\}\), where

[0078] S5. Initialize the cross-correlation vector according to the activity index.

[0079] Initialize the cross-correlation vector using the activity index \(\gamma(n)\) according to the following formula

[0080] n 0 = maxarg n (γ(n))

[0081] γ(n 0 ) = 0

[0082]

[0083] where γ(n) represents the activity index corresponding to the nth sampling moment, and n 0 represents the sampling moment corresponding to the maximum value of the activity index, and γ(n 0 ) = 0 means ensuring that the cross-correlation vector is initialized to different values multiple times, represents the value of the whitened surface electromyogram signal at the moment of n 0 moments, represents the cross-correlation vector. The activity index with subscript n 0 being set to 0 can prevent this value from being reused.

[0084] S6. Obtain a preset gradient function and learning rate, and perform iterative update on the cross-correlation vector.

[0085] Select as the gradient function, and at the same time set the learning rate to η = 0.01. According to the natural gradient descent method, the iterative formula for the cross-correlation vector can be obtained as:

[0086]

[0087]

[0088] where, represents the firing time series of the jth motor unit.

[0089] S7. Calculate the firing time series of the motor unit according to the updated cross-correlation vector and the whitened surface electromyogram signal.

[0090] After obtaining the updated cross-correlation vector, according to the gradient convolution kernel compensation algorithm, the firing time series of the motor unit can be calculated by the following formula:

[0091]

[0092] where, represents the cross-correlation vector, represents the correlation matrix, represents the whitened surface electromyogram signal.

[0093] S8. Take the obtained firing time series as the reference signal, and use the correlated constrained FastICA to correct the reference signal to obtain the optimized firing time series of the motor unit.

[0094] Take the obtained firing time series of the motor unit as the reference signal r and input it into the correlated constrained FastICA. The following optimization problem needs to be considered:

[0095]

[0096] where G is a non-polynomial function, and take G = logcosh(u). The second term in the objective function is a penalty term, and the penalty weight μ is a suitable positive constant. Use the Newton method to solve the above optimization problem, and the iterative formula for the decomposition coefficient vector w can be obtained:

[0097]

[0098] where,

[0099] After obtaining the decomposition coefficient vector, the optimized firing time series of the motor unit can be calculated therefrom:

[0100]

[0101] S9. Repeat S5 to S8 until no new firing time series of the motor unit can be decomposed.

[0102] The decomposition results of the simulated EMG signals with a signal-to-noise ratio (SNR) of 10 dB and a constant excitation level (MVC) of 10% in the present invention are as Figure 2 shown, and the decomposition results of the simulated EMG signals with a constant excitation level (MVC) of 30% are as Figure 3 shown. The decomposition results of the true firing time series, the gradient convolution kernel compensation method and the method in the present invention show that the surface EMG signal decomposition method based on gradient convolution kernel compensation and correlated constrained FastICA proposed in the present invention has a high decomposition accuracy.

[0103] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A surface electromyography signal decomposition method based on gradient convolution kernel compensation, characterized in that: The following steps are involved: S1, collect surface electromyography signals of multiple channels; S2, expanding the surface electromyographic signal according to a preset expansion factor to obtain an expanded surface electromyographic signal; S3, calculating a whitening matrix based on the expanded surface electromyographic signal, and performing whitening processing on the expanded surface electromyographic signal based on the whitening matrix to obtain a whitened surface electromyographic signal; S4, calculating the cross-correlation matrix according to the whitened surface electromyographic signal and initializing the activity index; S5, initializing the cross-correlation vector according to the activity index; S6, obtaining a preset gradient function and learning rate, and iteratively updating the cross-correlation vector; S7, calculating the firing time series of the motor unit according to the updated cross-correlation vector and the whitened surface electromyographic signal; S8, using the obtained firing time series as a reference signal, using the related constraint FastICA to correct the reference signal, and obtaining the optimized motor unit firing time series; S9, repeat S5 to S8 until no new motor unit firing time sequence can be decomposed.

2. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 1, characterized in that: The collected multi-channel surface electromyography signal can be expressed as: x=[x(1),x(2),x(3),…,x(n),…] where x(n)=[x1(n),x2(n),…,x M (n)] T represents the surface electromyographic signal collected at the nth sampling moment, x i (n) is the component on the i-th channel, and M represents the number of channels of the surface electromyography signal.

3. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 2 is characterized in that: The expanded surface electromyographic signal is: in It represents the surface electromyographic signal at the nth sampling moment after expansion, d is the preset expansion factor, the number of channels before expansion is M, and the number of channels after expansion is M(d+1).

4. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 3 is characterized in that: The expanded surface electromyography signal is whitened based on the whitening matrix, including: According to the expanded surface electromyography signal Calculate the covariance matrix, and calculate the eigenvalues ​​and eigenvectors of the covariance matrix; Arrange the eigenvalues ​​from large to small to form a diagonal matrix D, and arrange the eigenvectors corresponding to the eigenvalues ​​in order to form a characteristic matrix E, then the whitening matrix Q = sqrt(D) / E T , where sqrt() means calculating the square root, E T represents the transposed matrix of matrix E; Apply the whitening matrix Q to the expanded surface electromyographic signal Get the whitened surface electromyographic signal 5. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 4 is characterized in that: Calculate the cross-correlation matrix based on the whitened surface electromyographic signal and initialize the activity index, including: Based on the surface electromyographic signal after whitening The cross-correlation matrix is ​​calculated according to the following formula: Where E() represents mathematical expectation; Initialize the activity index to: γ={γ(n); n=1,2,3,…} in 6. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 5, characterized in that: Initialize the cross-correlation vector according to the activity index, including: n0=max arg n (γ(n)) γ(n0)=0 Wherein, γ(n) represents the activity index corresponding to the nth sampling time, n0 represents the sampling time corresponding to the maximum value of the activity index, and γ(n0)=0 means to ensure that the cross-correlation vector is repeatedly initialized to different values. represents the value of the whitened surface electromyographic signal at time n0, represents the cross-correlation vector.

7. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 6 is characterized in that: The iterative formula of the cross-correlation vector is: Among them, η represents the learning rate, represents the gradient function, and represents the firing time series of the jth motor unit.

8. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 7, characterized in that: According to the gradient convolution kernel compensation algorithm, the firing time series of the jth motor unit is: in, represents the cross-correlation vector, represents the correlation matrix, Represents the surface electromyographic signal after whitening.

9. The surface electromyography signal decomposition method based on gradient convolution kernel compensation according to claim 8, characterized in that: The obtained firing time series is used as the reference signal, and the reference signal is corrected using the related constraint FastICA to obtain the optimized motor unit firing time series, including: The obtained motor unit firing time series The reference signal r is input into the related constraint FastICA to construct the optimization problem: Where G is a non-polynomial function, G = logcosh(u), is a penalty term, and the penalty weight μ is a positive constant; Using Newton's method to solve the optimization problem, we can get the iterative formula of the decomposition coefficient vector w: in, The optimized motor unit release time series calculated based on the decomposition coefficient vector is: in, Represents the surface electromyographic signal after whitening.

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