Sparse representation and low-rank constraint electroencephalogram signal fast denoising model

Abstract

The embodiment of the invention discloses a rapid electroencephalogram signal denoising algorithm, relates to the technical field of signal denoising, and can effectively and rapidly improve the denoising effect of electroencephalogram signals. The method comprises the steps that a model based on sparse representation and low-rank constraint is proposed from an existing non-invasive noisy electroencephalogram signal sample to conduct denoising on the noisy electroencephalogram signal sample, so that the quality of electroencephalogram signals is improved, and then brain function anomaly detection is conducted. The method has the advantages of being high in denoising efficiency, good in denoising quality, rapid and the like, and can be applied to the preprocessing process of the electroencephalogram signals and the technical field of related signal denoising processing.

Description

Technical Field

[0001] The present application relates to the field of EEG signal denoising, and specifically designs a fast EEG signal denoising algorithm based on sparse representation and low-rank constraints. Background Art

[0002] Electroencephalogram (EEG) is a basic physiological signal of the human body, which contains a lot of useful physiological, psychological and medical information, and is of great significance for the diagnosis and treatment of brain diseases. In recent years, brain-computer interface (BCI) has become the focus of research in the field of brain science, and the acquisition of EEG signals is the key to BCI research. However, EEG signals are microvolt-level bioelectric signals, and they are also non-stationary and susceptible to noise interference. Therefore, it is particularly important to denoise EEG signals before using them.

[0003] The prior art proposes a method for denoising EEG signals based on wavelet transform. With its good time-frequency characteristics, the wavelet transform method can be applied to the analysis of non-stationary signals. First, the EEG signal is decomposed into sub-band signals of different frequencies by wavelet decomposition. Then, for the high-frequency sub-band where the noise is mainly concentrated, appropriate threshold processing or filtering methods are used to remove the noise. Finally, the processed sub-band signal is reconstructed by wavelet to obtain the denoised EEG signal. However, the selection of its wavelet basis and the number of decomposition layers is determined manually, and inappropriate selection may lead to the loss of effective information.

[0004] The prior art also proposes an EEG signal denoising method based on empirical mode decomposition (EMD). First, the complex EEG signal is adaptively decomposed into multiple intrinsic mode functions (IMFs) and a residual term through EMD. Subsequently, the IMF components containing high-frequency noise are identified and eliminated based on the spectral characteristics of each IMF or its correlation with the original signal. Finally, the remaining IMF components are recombined with the residual term to reconstruct a purer EEG signal. This process effectively removes noise interference, retains important signal features, and improves signal quality. However, the EMD method may be affected by the modal aliasing problem when processing EEG signals, that is, signals of different time scales may be mixed in the same IMF component, or signals of the same time scale are distributed in different IMF components, which will affect the denoising effect.

[0005] The prior art also proposes an EEG signal denoising method based on adaptive filtering, which effectively suppresses the interference components in the EEG signal by adjusting the filter parameters in real time to match and eliminate the noise characteristics. This method can automatically adapt to the changes in signals and noise without knowing the precise statistical characteristics of the noise in advance, thereby showing excellent denoising performance when processing non-stationary and nonlinear EEG signals. However, the performance of the adaptive filter is affected by its parameter settings and algorithm selection. If the parameters are improperly set or the algorithm is not selected appropriately, it may lead to poor filtering effects or the introduction of new noise. Summary of the invention

[0006] In order to solve the problem that the above-mentioned prior art has poor denoising effect on EEG signals, the present invention proposes a fast EEG signal denoising algorithm based on sparse representation and low rank constraint.

[0007] In order to solve the above technical problems, the technical solution of the present invention is as follows:

[0008] A fast EEG signal denoising algorithm based on sparse representation and low-rank constraint, comprising the following steps:

[0009] S1: Obtain EEG signal dataset

[0010] First, we select the experimental data of one of the subjects from the public BCI Competition IV data set 2a and label it as a clean EEG signal sample X;

[0011] S2: Noisy EEG signal sample

[0012] Use zero-mean additive noise w with a variance of σ as the noise sample, add σ to the clean EEG signal sample, and the zero-mean additive noise w constitutes the noisy EEG signal sample. Use the above method to test whether the obtained brain function signal contains noise. Usually, the empirical value σ obtained by actual calculation is 15;

[0013] S3: Constructing an EEG signal denoising model based on sparse representation and low-rank constraints

[0014] The EEG signal denoising model based on sparse representation and low-rank constraint is mainly composed of a sparse representation algorithm and a low-rank recovery algorithm;

[0015] S4: Model solution and reconstruction of denoised EEG signals

[0016] The noisy EEG signal is input into an EEG signal denoising model based on sparse representation and low-rank constraint, and the denoised EEG signal is output. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1This is a flowchart of an EEG signal denoising algorithm based on sparse representation and low-rank constraint in this application; DETAILED DESCRIPTION

[0018] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0019] This embodiment proposes an EEG signal denoising algorithm based on sparse representation and low-rank constraint. Figure 1 Schematic diagram of the process of the EEG signal denoising algorithm based on sparse representation and low rank constraint in this embodiment.

[0020] The EEG signal denoising algorithm based on sparse representation and low-rank constraint proposed in this embodiment includes the following steps:

[0021] S1: Obtain EEG signal dataset

[0022] First, we select the experimental data of one of the subjects from the public BCI Competition IV data set 2a and label it as a clean EEG signal sample X;

[0023] S2: Constructing noisy EEG signal samples

[0024] Use zero-mean additive noise w with a variance of σ as the noise sample, add σ to the clean EEG signal sample, and the zero-mean additive noise w constitutes the noisy EEG signal sample. Use the above method to test whether the obtained brain function signal contains noise. Usually, the empirical value σ obtained by actual calculation is 15;

[0025] S3: Constructing an EEG signal denoising model based on sparse representation and low-rank constraints

[0026] The fast EEG signal denoising model based on sparse representation and low-rank constraint is mainly composed of a sparse representation algorithm and a low-rank recovery algorithm;

[0027] S4: Model solution and reconstruction of denoised EEG signals

[0028] The noisy EEG signal is input into an EEG signal denoising model based on sparse representation and low-rank constraint, and the denoised EEG signal is output.

[0029] In the specific implementation process, sparse coding is first used to establish a non-local similarity model for the signal of a single channel, and a local similarity model is established for the signals between each channel, and then the denoised EEG signal can be obtained by using the linear combination of overcomplete dictionary atoms. In this process, only the local similarity between the EEG signals of each channel is used, which will reduce the denoising effect of the EEG signal. In response to this problem, the present invention introduces a low-rank constraint to the local similarity model to compensate for the deficiencies caused by the local similarity, and finally completes the EEG signal denoising to achieve a good EEG signal denoising effect.

[0030] Optionally, step S3 includes:

[0031] S3.1: Establish an EEG signal denoising model based on sparse representation:

[0032]

[0033] The first term in the formula is the fidelity term, which is used to measure the similarity between the denoised EEG signal and the input EEG signal. The size of μ is determined by the variance of the noise. The smaller the noise variance, the larger the value of μ should be to ensure that the denoised EEG signal is close enough to the input EEG signal. Otherwise, the smaller the value of μ is.

[0034] R i is a matrix vector used to extract from multi-channel EEG signals The signal blocks are of size N, where n<<N. Each signal block is reshaped into a column vector f i , we get the matrix F = [f1, f2…f N ].

[0035] S3.2: Add low-rank constraints to the sparse representation model for EEG signal denoising:

[0036] Single-channel EEG signals have non-local similarity, but EEG signals between channels have only local similarity. To compensate for the shortcomings of local similarity, the present invention adds low-rank constraints to the sparse representation framework to obtain an EEG signal denoising model based on sparse representation and low-rank constraints:

[0037]

[0038] The last rank function in the above formula is non-convex, so directly solving it cannot get the only optimal solution. In his doctoral thesis, Fazel proved that the nuclear norm is the tightest convex proxy of the rank function, and proposed a convex relaxation method that uses the nuclear norm to approximate the rank function and obtains a low-rank solution by solving a single nuclear norm convex optimization problem. The rank function in the above formula is approximated by the nuclear norm, so the above formula can be updated as:

[0039]

[0040] In the above formula, ||X|| * Represents the sum of the singular values ​​of the X matrix. In the process of solving the above formula, the advantages of non-local similarity and sparse representation are combined to more effectively remove the noise in the EEG signal. In order to facilitate the solution of the above formula, the present invention introduces an auxiliary variable W, and replaces the variable X in the last term of the above formula with W through the equality constraint X=W, so the formula can be updated as follows:

[0041]

[0042] The Lagrange multiplier method is used to transform the above constrained optimization problem into an unconstrained optimization problem:

[0043]

[0044] Optionally, step S4 includes:

[0045] S4.1: Solve for D and α by fixing the values ​​of X and W i :

[0046]

[0047] The solution process of the above formula is the process of dictionary learning and sparse coding. The present invention adopts KSVD algorithm to learn the dictionary and adopts OMP algorithm to obtain the optimal sparse coding α according to the learned dictionary.

[0048] S4.2: By fixing X, D, α i The value of W is used to solve:

[0049]

[0050] The common method for solving the above equation is to perform SVD decomposition on the X matrix, and then perform threshold shrinkage on the singular value elements obtained by the SVD decomposition, so as to reduce the mean square error between W and X as much as possible under the premise of ensuring that W has as low a rank as possible. The present invention uses a soft threshold method to shrink the singular value elements obtained by decomposition, and then solves W, that is:

[0051]

[0052] In the above formula, soft represents the soft threshold shrinkage operator, which is used as the singular value shrinkage function of X.

[0053] S4.3: In D, α i , solve X when W value is fixed:

[0054] By solving the above steps, we have obtained D, α i , W values, and substituting them into the denoising model can obtain the denoised EEG signal:

[0055]

[0056] S4.4: Solving the above equation, the approximate solution of the denoised EEG signal can be expressed as follows:

[0057]

[0058] In the above formula, α is all α iThe above solution process is one iteration. In order to obtain a better denoising effect, multiple iterations are usually required.

[0059] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for rapid denoising of EEG signals, characterized in that: The following steps are involved: S1: Obtain EEG signal dataset First, we select the experimental data of one of the subjects from the public BCI Competition IV data set 2a and label it as a clean EEG signal sample X; S2: Noisy EEG signal sample detection Use zero-mean additive noise w with a variance of σ as the noise sample, add σ to the clean EEG signal sample, and the zero-mean additive noise w constitutes the noisy EEG signal sample. Use the above method to test whether the obtained brain function signal contains noise. Usually, the empirical value σ obtained by actual calculation is 15; S3: Constructing a fast EEG signal denoising model based on sparse representation and low-rank constraints The EEG signal fast denoising model based on sparse representation and low-rank constraint is mainly composed of a sparse representation algorithm and a low-rank recovery algorithm; S4: Model solution and rapid reconstruction of denoised EEG signals The noisy EEG signal is input into an EEG signal denoising model based on sparse representation and low-rank constraint, and the denoised EEG signal is output.

2. The EEG signal denoising model based on sparse representation and low-rank constraint according to claim 1, characterized in that: In step S2, the noisy EEG signal samples are detected according to the following formula: X=Yw Where X represents the noisy EEG signal sample Y after removing the zero-mean additive noise, and w represents the noise sample.

3. The EEG signal denoising model based on sparse representation and low-rank constraint according to claim 1, characterized in that: The S3 steps include: S3.1: Establish an EEG signal denoising model based on sparse representation: The first term in the formula is the fidelity term, which is used to measure the similarity between the denoised EEG signal and the input EEG signal. The size of μ is determined by the variance of the noise. The smaller the noise variance, the larger the value of μ should be to ensure that the denoised EEG signal is close enough to the input EEG signal. Otherwise, the smaller the value of μ is. R i is a matrix vector used to extract from multi-channel EEG signals The signal blocks are of size N, where n<<N. Each signal block is reshaped into a column vector f i , we get the matrix F = [f1, f2…f N ]. S3.2: Add low-rank constraints to the sparse representation model for EEG signal denoising: Single-channel EEG signals have non-local similarity, but EEG signals between channels have only local similarity. To compensate for the shortcomings of local similarity, the present invention adds low-rank constraints to the sparse representation framework to obtain an EEG signal denoising model based on sparse representation and low-rank constraints: The last rank function in the above formula is non-convex, so directly solving it cannot get the only optimal solution. In his doctoral thesis, Fazel proved that the nuclear norm is the tightest convex proxy of the rank function, and proposed a convex relaxation method that uses the nuclear norm to approximate the rank function and obtains a low-rank solution by solving a single nuclear norm convex optimization problem. The rank function in the above formula is approximated by the nuclear norm, so the above formula can be updated as: In the above formula, ||X|| * Represents the sum of the singular values ​​of the X matrix. In the process of solving the above formula, the advantages of non-local similarity and sparse representation are combined to more effectively remove the noise in the EEG signal. In order to facilitate the solution of the above formula, the present invention introduces an auxiliary variable W, and replaces the variable X in the last term of the above formula with W through the equality constraint X=W, so the formula can be updated as follows: The Lagrange multiplier method is used to transform the above constrained optimization problem into an unconstrained optimization problem:

4. The EEG signal denoising model based on sparse representation and low-rank constraint according to claim 1, characterized in that: The S4 step includes: S4.1: Solve for D and α by fixing the values ​​of X and W i : The solution process of the above formula is the process of dictionary learning and sparse coding. The present invention adopts KSVD algorithm to learn the dictionary and adopts OMP algorithm to obtain the optimal sparse coding α according to the learned dictionary. S4.2: By fixing X, D, α i The value of W is used to solve: The common method for solving the above equation is to perform SVD decomposition on the X matrix, and then perform threshold shrinkage on the singular value elements obtained by the SVD decomposition, so as to reduce the mean square error between W and X as much as possible under the premise of ensuring that W has as low a rank as possible. The present invention uses a soft threshold method to shrink the singular value elements obtained by decomposition, and then solves W, that is: In the above formula, soft represents the soft threshold shrinkage operator, which is used as the singular value shrinkage function of X. S4.3: In D, α i , solve X when W value is fixed: By solving the above steps, we have obtained D, α i , W values, and substituting them into the denoising model can obtain the denoised EEG signal: S4.4: Solving the above equation, the approximate solution of the denoised EEG signal can be expressed as follows: In the above formula, α is all α i The above solution process is one iteration. In order to obtain a better denoising effect, multiple iterations are usually required.

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