Electroencephalogram signal time-frequency representation method based on scale adaptive sparse multi-wavelet

Abstract

The invention provides an electroencephalogram signal time-frequency representation method based on scale adaptive sparse multi-wavelets, which comprises the following steps of: modeling an electroencephalogram signal based on a time-varying autoregression model, and representing a time-varying parameter by a time-invariant parameter and a primary function; the adaptive scale of the primary function is adaptively selected according to the characteristics of the electroencephalogram signal, so that the electroencephalogram signal is converted into a high-resolution time-frequency estimation result; according to the method, the appropriate scale can be adaptively selected according to the characteristics of the signals, so that the constructed time-varying model can accurately track the time-varying parameters and further convert the time-varying parameters into a high-resolution time-frequency estimation result, a finer electroencephalogram signal time-frequency result can be provided, and a foundation is laid for application based on time-frequency analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of electroencephalogram (EEG) signal processing, and in particular to a time-frequency representation method of EEG signals based on scale-adaptive sparse multiwavelets. Background Art

[0002] Various bioelectrical signals of the human body, such as electroencephalogram (EEG) signals, electromyogram (EMG) signals, and electrooculogram (EOG) signals, etc., all contain rich physiological information of the human body. Among them, EEG signals can detect the electrical activities of the cerebral cortex through electrodes and can directly reflect the current activity state of the brain. In addition, EEG signals also have advantages such as non-invasiveness, high time resolution, and high sensitivity. Therefore, EEG signals have been widely applied to various brain-related researches, such as sleep research, disease monitoring, and movement control mechanisms, etc.

[0003] However, EEG signals are typical non-stationary signals, and it is difficult to obtain intuitive and effective information by directly analyzing the original EEG signals. Since EEG signals have high time resolution and the collective activities of neurons will show rhythmic oscillations at different frequencies, it is a feasible method to analyze EEG signals by combining time information and frequency information. Through the time-frequency analysis technology of EEG signals, the dynamic characteristics of different rhythms changing with time can be revealed. For healthy people, the time-frequency analysis technology can be used to study attention, brain processing methods, and cognitive behaviors, etc., which is beneficial to expounding the working mechanism of the brain; for patients, favorable features can be extracted from the time-frequency diagrams of EEG signals to train classifiers to achieve intelligent rehabilitation training based on human-computer interaction; comparing the time-frequency information differences between patients and healthy people is also beneficial to revealing possible individual differences or cortical abnormalities, which is of great significance for diagnosing certain nervous system diseases and evaluating cognitive functions, etc.

[0004] Among the currently published or disclosed time-frequency representation technologies of EEG signals, they mainly include non-parametric methods and parametric methods. Non-parametric methods mainly include short-time Fourier transform, wavelet transform, etc. These methods are easily restricted by the window size and basis functions and cannot provide high-resolution time-frequency results. Parametric methods obtain parameters by identifying time-varying models and then use spectral estimation methods to convert the time-varying parameters into time-frequency results, mainly including adaptive methods and basis function expansion methods. Among them, adaptive methods mainly include recursive least squares method and Kalman filtering algorithm, etc. When the signal changes rapidly, there will be an obvious lag in the adaptive method for tracking time-varying parameters, and it is difficult to ensure the time-frequency resolution.

[0005] Compared with the adaptive method, the basis function expansion method can track various types of time-varying parameters more effectively. The commonly used methods mainly include multi-scale radial basis and multi-B-spline wavelet basis. Among them, the multi-scale radial basis approximates different signals by changing the scale of the radial basis function. However, due to the smoothness of the function itself, its performance in tracking abrupt signals is not as good as that of non-smooth functions such as Harr wavelets. The multi-B-spline wavelet has various properties, but its scale is fixed, which limits the flexibility in parameter estimation. Both of these two methods may lose instantaneous information, resulting in inaccurate time-frequency estimation results and making it difficult to objectively reflect the dynamic characteristics of the brain. Summary of the Invention

[0006] The present invention proposes a method for time-frequency representation of electroencephalogram (EEG) signals based on scale-adaptive sparse multi-wavelets, which can adaptively select appropriate scales according to the characteristics of the signals, so that the constructed time-varying model can accurately track time-varying parameters, and then be transformed into high-resolution time-frequency estimation results, providing more refined time-frequency results of EEG signals and laying a foundation for applications based on time-frequency analysis.

[0007] The present invention adopts the following technical solutions.

[0008] A method for time-frequency representation of electroencephalogram (EEG) signals based on scale-adaptive sparse multi-wavelets, the method includes modeling the EEG signals based on a time-varying autoregressive model, and its time-varying parameters are represented by time-invariant parameters and basis functions; by adaptively selecting the adaptation scale of the basis functions according to the characteristics of the EEG signals, it is transformed into high-resolution time-frequency estimation results.

[0009] The method includes the following steps;

[0010] Step S1, signal collection and preprocessing: Use an EEG cap to collect EEG signals in the target scenario, and perform low-pass, power frequency notch filtering and downsampling on the signals;

[0011] Step S2, selection of important regression terms: Model the processed EEG signals as a time-invariant autoregressive model with time lags, and assign weights to each regression term by combining sparse Bayesian learning and information entropy, and select important regression terms according to the weights;

[0012] Step S3, construction of a time-varying model based on basis functions: According to the determined important regression terms, re-model the EEG signals as a time-varying autoregressive model with time lags, and its time-varying parameters are represented by the product of time-invariant parameters and basis functions, and perform scale-adaptive adjustment on the basis functions based on an improved genetic algorithm.

[0013] Step S4, Estimation of time-varying parameters and time-frequency estimation: Use the least squares method to estimate the only unknown in the time-varying autoregressive model - the time-invariant parameter, and then reconstruct the time-varying parameter by combining the basis functions after scale transformation. Use the parametric spectral estimation method to transform the time-varying parameter into a time-frequency diagram.

[0014] In step S1, the target scenarios include sleep scenarios, emotional scenarios, and exercise scenarios.

[0015] In step S1, use the EEGLAB toolbox in Matlab to preprocess the EEG signals. The preprocessing methods include band-pass filtering from 0.5 - 80 Hz, power frequency notch filtering at 50 Hz, and downsampling to 250 Hz.

[0016] In step S2, use the time-invariant autoregressive model to model the EEG signals preprocessed in step S1. The formula is:

[0017]

[0018] where y(t) represents the EEG signal at the current moment, y(t - i) represents the EEG signal with a lag of i time durations. p is the model order, θ i represents the time-invariant parameter, and e(t) is a sequence of independent and normally distributed random variables with a mean of 0 and a variance of ; Φ 1 = [y(t - 1),..., y(t - p)], Θ = [θ 1 ,..., θ p .

[0019] During the modeling process of step S2, to select the appropriate model order, that is, the p value, use sparse Bayesian learning to obtain the sparse parameters, which are expressed by the following formula:

[0020]

[0021] where μ is the Lagrange coefficient with a value of 0.1, λ is the regularization parameter with a value of 0.1, G is the p×p identity matrix, v k and d k are 0 sequences with p rows and 1 column. Retain the time-invariant parameters of each iteration to form an iteration matrix;

[0022] Normalize the iteration matrix by the regression terms and calculate the information entropy of the iteration parameter matrix, which is expressed by the formula:

[0023]

[0024] where K represents the number of iterations, represents the normalized iteration parameter, represents a value of The probability; b is a constant with a value of 2. The quartile method is used to extract the outliers in the entropy value sequence, and the regression terms corresponding to the outliers are the final model terms. The number of model terms is the p-value, denoted as p 1 .

[0025] In step S3, after obtaining the important regression terms and the model order, the EEG signal is re-established as a time-varying autoregressive model. To facilitate the estimation using the least squares method, the time-varying parameters are transformed into the product of time-invariant parameters and basis functions by the method of basis function expansion, expressed as:

[0026]

[0027] where represents the known structure, G 1 is the row vector of unknown time-invariant parameters, and the superscript T is the matrix transpose; y i represents the i-th retained important regression term.

[0028] In step S3, to adapt to the changing time-varying parameters, the basis function is selected as a multi-B-spline wavelet, and the formula is:

[0029]

[0030] where j represents the scale factor, k represents the displacement factor, and B r is the r-th order B-spline function, and r usually takes values in [2, 3, 4] to form a multi-B-spline wavelet; its recursive form is defined as:

[0031]

[0032] When r = 1, the B-spline is the Harr wavelet, defined as:

[0033]

[0034] In step S3, to improve the description ability of B-spline wavelet basis for different signals, an improved genetic algorithm is used to find the optimal scale, and the multi-B-spline wavelet is subjected to central scale transformation using the optimal scale. Specifically: according to the displacement factor, the number of scales to be transformed is set, each parameter is represented by 5-bit binary, the population size is set to 100, population initialization is performed, and the fitness is the root mean square error between the target value and the predicted value; after the selection operation, it is judged whether the optimal individual is selected. If not, the optimal individual is used to replace the worst selected individual; subsequently, single-point crossover operation is performed; finally, the population is clustered into three sub-populations of high, medium, and low according to the fitness, and the overall optimal value (gbest) and the class center (pbest) of each sub-population are recorded; when the mutation operation is performed, the mutation individual is selected according to the probability, the individual is converted from binary to decimal, and the mutation is performed according to the following formula:

[0035] x new =c 1 x + c 2 (pbest - x) + c 3 (gbset - x) Formula 8;

[0036] Among them, c 1 -c 3 respectively represent the inheritance degree of the current state, the influence degree of the individual by the sub-population, and the influence degree of the individual by the entire population;

[0037] When the optimal RMSE values are equal for more than 3 times, half of the individuals with poor fitness in the current population are replaced with random individuals, and one round of iteration is performed; if the optimal individual in the new population is better than the optimal individual in the non-replaced population, the replacement is valid and the iteration continues; if the optimal individual in the new race performs poorly, the replacement is invalid and the original population is used for continued iteration;

[0038] After obtaining the optimal scale, the peak of a single basis function is found, and centered on the peak, the basis function is scaled left and right using the scale.

[0039] In step S4, after constructing a complete statistical model, i.e., the TVAR model, for analyzing the dynamic relationship between multiple time series through steps S1, S2, and S3, the time-invariant parameter g i，m is estimated using the least squares method, and substituting it into Formula 4 to obtain the estimated value of the time-varying parameter After that, time-frequency estimation is performed based on the parameters, and the formula is

[0040]

[0041] Among them, f s is the sampling frequency, is the variance of the estimation error.

[0042] The present invention provides a method for time-frequency representation of electroencephalogram (EEG) signals based on scale-adaptive multi-wavelet bases. First, by combining information entropy and a sparse Bayesian learning iterative matrix, weights are assigned to each autoregressive term, and important regression terms are selected therefrom to ensure the generalization of the model. Then, multi-B-spline wavelet bases are selected as basis functions, and an improved genetic algorithm is used to find the optimal scale to achieve the adaptive scaling of the basis functions, thereby improving the description ability of the basis functions for different signals. Finally, through a parametric spectral estimation method, the accurately tracked time-varying parameters are transformed into a high-resolution time-frequency map, which is beneficial for subsequent analysis. This method reduces the complexity of parameter selection and can provide better time-frequency estimation results, greatly facilitating practical applications.

[0043] The present invention has a wide range of applications. From the perspective of healthy people, the present invention can provide the time-frequency characteristics of healthy people in various situations, including sleep, emotions, movements, etc., which helps to understand the mechanism of the brain in processing information and subsequent control in all aspects, laying a foundation for the research on brain mechanisms and brain-like control; from the perspective of patients, the present invention can help doctors in disease diagnosis and research on the pathogenesis of diseases; at the same time, time-frequency features can also be extracted to train classifiers and applied in human-computer interaction. In short, the present invention can provide more refined time-frequency results of EEG signals, laying a foundation for applications based on time-frequency analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The present invention will be further described in detail below with reference to the drawings and specific embodiments:

[0045] FIG Figure 1 is a schematic flowchart of the scale-adaptive sparse multi-wavelet time-frequency representation method of the present invention;

[0046] FIG Figure 2 is a schematic diagram of scale optimization using an improved genetic algorithm in the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] As shown in the figure, a method for time-frequency representation of EEG signals based on scale-adaptive sparse multi-wavelets, the method includes modeling EEG signals based on a time-varying autoregressive model, and its time-varying parameters are represented by time-invariant parameters and basis functions; by adaptively selecting the adaptation scale of the basis functions according to the characteristics of the EEG signals to be transformed into high-resolution time-frequency estimation results.

[0048] The method includes the following steps;

[0049] Step S1, signal collection and preprocessing: Use an EEG cap to collect EEG signals in the target scenario, and perform low-pass, power frequency notch filtering, and downsampling on the signals;

[0050] The processed EEG signal data is used for subsequent modeling;

[0051] Step S2, Selection of important regression terms: Model the processed EEG signals as a time-invariant autoregressive model with time lags, assign weights to each regression term by combining sparse Bayesian learning and information entropy, and select important regression terms according to the weights;

[0052] Step S3, Construction of time-varying model based on basis functions: According to the determined important regression terms, re-model the EEG signals as a time-varying autoregressive model with time lags, where the time-varying parameters are represented by the product of time-invariant parameters and basis functions, and perform scale adaptive adjustment on the basis functions based on an improved genetic algorithm.

[0053] Step S4, Estimation of time-varying parameters and time-frequency estimation: Use the least squares method to estimate the only unknown in the time-varying autoregressive model - the time-invariant parameters, then reconstruct the time-varying parameters in combination with the basis functions after scale transformation, and convert the time-varying parameters into a time-frequency diagram using the parametric spectral estimation method.

[0054] In step S1, the target scenarios include sleep scenarios, emotional scenarios, and motion scenarios.

[0055] In step S1, use the eeglab toolbox in Matlab to perform data preprocessing on the EEG signals. The preprocessing methods include band-pass filtering from 0.5 - 80 Hz, power frequency notch filtering at 50 Hz, and downsampling at 250 Hz.

[0056] In step S2, use the time-invariant autoregressive model to model the EEG signals preprocessed in step S1. The formula is:

[0057]

[0058] Among them, y(t) represents the EEG signal at the current moment, and y(t - i) represents the EEG signal with a lag of i time durations. p is the model order, θ i represents the time-invariant parameter, and e(t) is a sequence of independent and normally distributed random variables with a mean of 0 and a variance of ; Φ 1 = [y(t - 1),..., y(t - p)], Θ = [θ 1 ,..., θ p .

[0059] During the modeling process of step S2, to select an appropriate model order, that is, the p value, obtain sparse parameters using sparse Bayesian learning, which is expressed by the following formula:

[0060]

[0061] Among them, μ is the Lagrangian coefficient with a value of 0.1, λ is the regularization parameter with a value of 0.1, G is the p×p identity matrix, v k and d k are 0 sequences of p×1. The time-invariant parameters of each iteration are retained to form an iteration matrix;

[0062] The iteration matrix is normalized according to the regression terms, and the information entropy of the iteration parameter matrix is calculated, which is expressed by the formula:

[0063]

[0064] Among them, K represents the number of iterations, represents the normalized iteration parameter, represents the probability with a value of ; b is a constant with a value of 2. The quartile method is used to extract the outliers in the entropy value sequence, and the regression terms corresponding to the outliers are the final model terms. The number of model terms is the p value, denoted as p 1 .

[0065] In step S3, after obtaining the important regression terms and the model order, the EEG signal is re-established as a time-varying autoregressive model. To facilitate the estimation using the least squares method, the time-varying parameters are transformed into the product of time-invariant parameters and basis functions by the method of basis function expansion, which is expressed as:

[0066]

[0067] Among them, represents the known structure, G 1 is the row vector of unknown time-invariant parameters, and the superscript T is the matrix transpose; y i represents the i-th retained important regression term.

[0068] In step S3, to adapt to the variable time-varying parameters, the basis function is selected as a multi-B-spline wavelet, and the formula is:

[0069]

[0070] Among them, j represents the scale factor, k represents the displacement factor, B r is the r-th order B-spline function, and r usually takes values in [2, 3, 4] to form a multi-B-spline wavelet; its recursive form is defined as:

[0071]

[0072] When r = 1, the B-spline is the Harr wavelet, which is defined as:

[0073]

[0074] In step S3, in order to improve the description ability of B-spline wavelet basis for different signals, an improved genetic algorithm is used to find the optimal scale, and the optimal scale is used to perform center scale transformation on multiple B-spline wavelets, specifically: the number of scales to be transformed is set according to the displacement factor, each parameter is represented by 5 bits of binary, the population number is set to 100, the population is initialized, and the fitness is the root mean square error between the target value and the predicted value; after the selection operation, it is determined whether the best individual is selected, if not selected, the best individual is replaced by the worst individual selected; then, a single-point crossover operation is performed; finally, the population is clustered into three sub-populations of high, medium and low according to the fitness, and the overall optimal value (gbest) and the class center (pbest) of each sub-population are recorded; when the mutation operation is performed, the mutation individual is selected according to the probability, the individual is converted from binary to decimal, and the mutation is performed according to the following formula:

[0075] x new =c 1 x+c 2 (pbest-x)+c 3 (gbset-x) Formula 8;

[0076] Among them, c 1 -c 3 They respectively represent the degree of inheritance of the current state, the degree to which the individual is influenced by the subpopulation, and the degree to which the individual is influenced by the entire population;

[0077] When the optimal RMSE values ​​for more than three times are equal, half of the individuals with poor fitness in the current population are replaced with random individuals, and one round of iteration is performed; if the optimal individual of the new population is better than the optimal individual of the unreplaced population, the replacement is effective and the iteration continues; if the optimal individual of the new population performs poorly, the replacement is invalid and the original population is used to continue the iteration;

[0078] After obtaining the optimal scale, find the peak value of a single basis function, and use the scale to scale the basis function left or right with the peak value as the center.

[0079] In step S4, after a complete statistical model for analyzing the dynamic relationship between multiple time series, namely the TVAR model, is constructed through steps S1, S2, and S3, the time-invariant parameter g is estimated using the least squares method. i，m , substituting it into Formula 4, we get the estimated value of the time-varying parameter After that, the time-frequency estimation is performed based on the parameters, and the formula is

[0080]

[0081] in, f s is the sampling frequency, is the variance of the estimation error.

[0082] This example is a method for time-frequency representation of EEG signals based on scale-adaptive multi-wavelet bases. The specific process of using it is as follows: First, obtain the EEG signals in the target scenario. After low-frequency, power-frequency notch filtering, and downsampling processing, establish the EEG signals as time-invariant autoregressive models, assign weights to each autoregressive term by combining sparse Bayesian learning and information entropy, and use the quartile method to select important candidate items; Subsequently, according to the selected important candidate items, re-express the EEG signals as time-varying autoregressive models, where the time-varying parameters are represented by the product of the basis functions and the time-invariant parameters; Select the basis function as the multi-B-spline wavelet basis, and use an improved genetic algorithm for scale optimization, and adaptively scale the B-spline wavelet basis based on the optimized scale; Estimate the time-invariant parameters using the least squares method, and obtain the time-varying parameters by combining the basis functions; Finally, use the parametric spectral estimation method to convert the time-varying parameters into high-resolution time-varying results.

Claims

1. A method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet, characterized by: The method includes modeling of EEG signals based on a time-varying autoregressive model, wherein time-varying parameters are represented by time-invariant parameters and basis functions; and converting the basis functions into high-resolution time-frequency estimation results by adaptively selecting the adaptation scale of the basis functions according to the characteristics of the EEG signals.

2. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 1, characterized in that: The method comprises the following steps: Step S1, signal collection and preprocessing: using an EEG cap to collect EEG signals in the target scene, and performing low-pass, power frequency notch and down-sampling processing on the signals; Step S2, selection of important regression items: modeling the processed EEG signal as a time-invariant autoregressive model with time lag, combining sparse Bayesian learning and information entropy to assign weights to each regression item, and selecting important regression items according to the weights; Step S3, constructing a time-varying model based on basis functions: according to the determined important regression terms, the EEG signal is remodeled into a time-varying autoregressive model with time lag, whose time-varying parameters are represented by the product of the time-invariant parameters and the basis functions, and the basis functions are scale-adaptively adjusted based on the improved genetic algorithm. Step S4, estimation of time-varying parameters and time-frequency estimation: Use the least squares method to estimate the only unknown number in the time-varying autoregressive model, the time-invariant parameter, and then reconstruct the time-varying parameter in combination with the scaled basis function, and use the parameterized spectrum estimation method to convert the time-varying parameter into a time-frequency diagram.

3. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 2, characterized in that: In step S1, the target scenes include sleeping scenes, emotional scenes and sports scenes.

4. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 2, characterized in that: In step S1, the EEGlab toolbox in Matlab is used to preprocess the EEG signal. The preprocessing method includes 0.5-80 Hz bandpass filtering, 50 Hz power frequency notch, and 250 Hz downsampling.

5. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 2, characterized in that: In step S2, the EEG signal preprocessed in step S1 is modeled using a time-invariant autoregressive model, and the formula is: Among them, y(t) represents the EEG signal at the current moment, and y(ti) represents the EEG signal with a lag of i time. p is the model order, θ i represents a time-invariant parameter, e(t) is a parameter with a mean of 0 and a variance of is a sequence of independent and normally distributed random variables; Φ1=[y(t-1),...,y(tp)], Θ=[θ1,...,θ p ].

6. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 5, characterized in that: In the modeling process of step S2, in order to select the appropriate model order, that is, the p value, sparse parameters are obtained by using sparse Bayesian learning, which is expressed as the following formula: Among them, μ is the Lagrange coefficient with a value of 0.1, λ is the regularization parameter with a value of 0.1, G is the identity matrix with p rows and p columns, and v k and d k is a zero sequence with p rows and 1 column. The time-invariant parameters of each iteration are retained to form an iteration matrix; The iterative matrix is ​​normalized according to the regression term, and the information entropy of the iterative parameter matrix is ​​calculated, which can be expressed as: Where K represents the number of iterations, represents the normalized iteration parameter, Indicates that the value is The probability of; b is a constant, the value is 2. The quartile method is used to extract the outliers in the entropy value sequence, and the regression term corresponding to the outlier is the final model term. The number of model terms is the p value, recorded as p1.

7. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 2, characterized in that: In step S3, after obtaining the important regression terms and model order, the EEG signal is re-established as a time-varying autoregressive model. In order to facilitate the estimation using the least squares method, the time-varying parameters are transformed into the product of the time-invariant parameters and the basis function using the basis function expansion method, expressed as: in, represents a known structure, G1 is the row vector of unknown time-invariant parameters, and the superscript T is the matrix transpose; y i represents the i-th retained important regression term.

8. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 7, characterized in that: In step S3, in order to adapt to the variable time-varying parameters, the basis function is selected as a multi-B-spline wavelet, and the formula is: Among them, j represents the scale factor, k represents the displacement factor, and B r is an r-order B-spline function, where r is usually [2, 3, 4], forming a multi-B-spline wavelet; its recursive form is defined as: When r = 1, the B-spline is the Harr wavelet, defined as:

9. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 8, characterized in that: In step S3, in order to improve the description ability of the B-spline wavelet basis for different signals, an improved genetic algorithm is used to find the optimal scale, and the optimal scale is used to perform a central scale transformation on the multiple B-spline wavelets, specifically: The number of scales to be transformed is set according to the displacement factor. Each parameter is represented by 5 bits of binary. The population size is set to 100, and the population is initialized. The fitness is the root mean square error between the target value and the predicted value. After the selection operation, it is determined whether the best individual is selected. If not, the best individual is replaced by the worst individual. Then, a single-point crossover operation is performed. Finally, the population is clustered into three sub-populations of high, medium and low according to fitness, and the overall optimal value (gbest) and the class center (pbest) of each sub-population are recorded; when performing mutation operation, the mutation individuals are selected according to probability, the individuals are converted from binary to decimal, and mutation is performed according to the following formula: x new =c1x+c2(pbest-x)+c3(gbest-x) Formula 8; Among them, c1-c3 represent the degree of inheritance of the current state, the degree to which the individual is affected by the subpopulation, and the degree to which the individual is affected by the entire population; When the optimal RMSE values ​​for more than three times are equal, half of the individuals with poor fitness in the current population are replaced with random individuals, and one round of iteration is performed; if the optimal individual of the new population is better than the optimal individual of the unreplaced population, the replacement is effective and the iteration continues; if the optimal individual of the new population performs poorly, the replacement is invalid and the original population is used to continue the iteration; After obtaining the optimal scale, find the peak value of a single basis function, center it on the peak value, and use the scale to scale the basis function left and right.

10. The method for time-frequency representation of EEG signals based on scale-adaptive sparse multiwavelet according to claim 2, characterized in that: In step S4, after the complete TVAR model is constructed through steps S1, S2, and S3, the time-invariant parameter g is estimated using the least squares method. i，m , substituting it into Formula 4, we get the estimated value of the time-varying parameter After that, the time-frequency estimation is performed based on the parameters, and the formula is in, f s is the sampling frequency, is the variance of the estimation error.

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