CN114259240A - Electroencephalogram signal dictionary learning method based on improved experience wavelet transformation - Google Patents
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Abstract
The invention discloses an electroencephalogram signal dictionary learning method based on improved experience wavelet transformation, which comprises the following steps: acquiring an electroencephalogram signal data set; dividing signals in the electroencephalogram signal data set into electroencephalogram signal segments with the same length; dividing the electroencephalogram signal fragments into a plurality of intrinsic mode components by using an improved empirical wavelet transform mode, wherein the intrinsic mode components can reflect the essential characteristics of the original electroencephalogram signals; screening the essential characteristics of the original electroencephalogram signals and putting the essential characteristics into an intrinsic mode component set; randomly selecting k samples from the eigenmode component set as a centroid, performing dictionary learning by using a k-mean singular value decomposition method, and outputting a trained dictionary; and reconstructing the electroencephalogram signal at a reconstruction end by using the trained dictionary. According to the method and the device, the dictionary can perform more optimal sparse representation on the electroencephalogram characteristics, and meanwhile, the characteristics of the signal are taken into consideration, so that the dependence of the learning dictionary on training samples is reduced, and the reconstruction accuracy is improved.
Description
Technical Field
The invention relates to the technical field of electroencephalogram signal processing, in particular to an electroencephalogram signal dictionary learning method based on improved empirical wavelet transformation and K-mean singular values.
Background
EEG (electroencephalogram) is a complex bioelectricity signal, and through deep analysis and research on EEG, the information processing process of human brain can be better understood, and the exploration of people on various aspects such as cognition of cranial nerve structures and physiological activities, reasonable application of EEG and the like is accelerated. In the traditional method, signals are sampled according to the Nyquist sampling theorem, then compressed and encoded, and finally decompressed at a receiving end to obtain original signals. This method inevitably generates a large amount of signal data, and it is difficult to transmit and store the signal data. Therefore, the research on the rapid and efficient electroencephalogram signal acquisition mode has great practical significance and application value. In order to overcome the defects of the traditional compression sampling mode, D.L.Donoho et al propose a compression sensing technology at the beginning of the 21 st century, and the acquisition mode saves storage space, reduces power consumption required during signal acquisition and transmission, reduces the pressure of an acquisition system, improves the durability of the system, improves the aspect of system hardware, reduces the volume of the system and enhances the portability of the system.
In the compressed sensing theory, the more sparse the coefficient of the electroencephalogram signal under the dictionary, the higher the signal reconstruction quality, so that it is very important to obtain the dictionary matched with the signal characteristics by which method. Dictionary selection is one of important research contents of signal compression sensing, and a dictionary obtaining mode can be divided into two categories: an analysis method and a learning method. The analytic method uses some mathematical transformations and proper amount of parameters to construct a dictionary, and has the advantages of no complexity, simpler calculation and obvious defects. In recent years, the study of a learning method is greatly developed, and the method continuously updates atoms in a dictionary through information in a learning signal, so that the atoms contain more abundant information and are more fit with the characteristics of electroencephalogram signals.
With the progress of research in the field of Dictionary learning, researchers have proposed a number of effective Dictionary learning methods, including earlier Multi Component Dictionary (MCD) dictionaries, Singular Value Decomposition (SVD) dictionaries, and the like. Mallat S et al, 1993, described the concept of an overcomplete dictionary for the first time and proposed the use of a matching pursuit algorithm to solve the sparse representation problem of an overcomplete dictionary. AHARON M first proposed a K-singular value decomposition (K-SVD) algorithm in 2006, which is a sparse representation Method for adaptive dictionary learning, and subsequently Engan et al proposed a Method of optimal orientation (MOD) algorithm. At present, the most used dictionary learning method is a K-SVD algorithm, which is slightly different from an MOD algorithm, and the K-SVD algorithm updates dictionary atoms column by column instead of simultaneously updating the whole dictionary, so that an over-complete dictionary which can sparsely express signals is learned. Wujiangning et al learn the electroencephalogram signal data set by using a K-SVD optimized learning algorithm to obtain an over-complete dictionary of multi-channel electroencephalogram signals. The scholars at home and abroad add the signal characteristics to dictionary learning instead of learning the dictionary by using the signal, thereby improving the effect of signal reconstruction. In order to fit the characteristics of electroencephalogram signals, highly-sophisticated and other people perform dictionary learning on modal components obtained by using Empirical Mode Decomposition (EMD) on audio signals, so that the dictionary sparse representation performance is better.
In summary, although the existing dictionary learning method can perform sparse representation on electroencephalogram signals, the quality of the signals after reconstruction needs to be improved, meanwhile, different testers have large differences of the signals at different times, and if the characteristics of the signals are not considered, the dictionaries are learned by the signals, so that the learning dictionaries have high dependence on training samples, and the reconstruction accuracy is low. Therefore, the dictionary learning method needs to be studied in depth.
Disclosure of Invention
Aiming at the problem that the existing dictionary learning method is low in electroencephalogram sparse representation performance, the invention provides an electroencephalogram dictionary learning method (EEG Empirical Wavelet Transform And K-Singular Value-based EEG-KSVD) based on improved Empirical Wavelet Transform, so that the dictionary can perform better sparse representation on electroencephalogram characteristics, And meanwhile, the characteristics of the signal are taken into consideration, the dependence of the learning dictionary on training samples is reduced, And the reconstruction accuracy is improved.
In order to achieve the purpose, the technical scheme of the application is as follows: the electroencephalogram signal dictionary learning method based on improved experience wavelet transform comprises the following steps:
acquiring an electroencephalogram signal data set;
dividing signals in the electroencephalogram signal data set into electroencephalogram signal segments with the same length;
dividing the electroencephalogram signal fragments into a plurality of intrinsic mode components by using an improved empirical wavelet transform mode, wherein the intrinsic mode components can reflect the essential characteristics of the original electroencephalogram signals;
screening the essential characteristics of the original electroencephalogram signals and putting the essential characteristics into an intrinsic mode component set;
randomly selecting k samples from the eigenmode component set as a centroid, namely randomly initializing k atoms, performing dictionary learning by using a k-mean singular value decomposition method, and outputting a trained dictionary;
and reconstructing the electroencephalogram signal at a reconstruction end by using the trained dictionary.
Further, the improved empirical wavelet transform method specifically includes:
performing interpolation operation on the electroencephalogram signals, and selecting extreme points by adopting a spectrum envelope curve;
adaptively determining an amplitude threshold value H according to an Otsu criterion;
judging the local extremum by using the amplitude threshold H, wherein subscripts corresponding to extremums larger than the amplitude threshold are regarded as useful boundaries, and corresponding frequency bands are regarded as effective frequency bands of the analyzed electroencephalogram signals;
and counting the useful boundaries to obtain an effective frequency band interval and obtain a decomposition modal number Z.
Further, the characteristic of the nature of the original electroencephalogram signal is screened, and the method specifically comprises the following steps: obtaining a correlation coefficient between each intrinsic mode component and other intrinsic mode components by using the following formula, then obtaining an average correlation coefficient of each intrinsic mode component and normalizing to [0,1], setting the absolute value of the correlation coefficient to be less than 0.5 as weak correlation, and selecting a mode with the correlation degree of less than 0.5;
in the above formula, Cov (x)i,xj) Represents the covariance of the ith and jth modes, Var [ x ]i]And Var [ x ]j]The variance of the eigenmode components of the ith and j empirical wavelet decompositions is respectively represented.
Due to the adoption of the technical scheme, the invention can obtain the following technical effects: the invention fully considers the characteristics of the electroencephalogram signals, reduces the dependence of dictionary learning on the electroencephalogram signals, and performs dictionary learning by using intrinsic mode components obtained by an improved experience wavelet transform mode to replace signals. Firstly, decomposing an electroencephalogram signal by using an improved empirical wavelet transform method to obtain an intrinsic mode component; secondly, screening the intrinsic mode components; then, a dictionary learning method based on K-means singular value decomposition is used for generating an adaptive dictionary for the selected mode, and unsupervised dictionary learning is achieved. The method improves the sparse representation capability and accuracy of the dictionary, and further improves the quality of electroencephalogram signal reconstruction.
Drawings
FIG. 1 is a flow chart of determining the number of segments for an improved empirical wavelet transform;
FIG. 2 is a block diagram of an EEWT-KSVD-based dictionary learning system;
FIG. 3 is a section of electroencephalogram signal with 256 sampling points;
FIG. 4 is a graph of spectral edge segmentation for the signal of FIG. 3 in three ways;
FIG. 5 is a diagram of modal components obtained by an empirical wavelet transform method;
FIG. 6 is a diagram of modal components obtained by a cubic spline-empirical wavelet transform method;
FIG. 7 is a diagram of modal components resulting from an improved empirical wavelet transform;
FIG. 8 is a comparison graph of electroencephalogram signals before and after reconstruction by four dictionary methods.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples: the present application is further described by taking this as an example. The embodiment of the invention is implemented on the premise of the technical scheme of the invention, and provides an electroencephalogram signal dictionary learning method based on improved empirical wavelet transform, which comprises the following specific steps:
empirical Wavelet Transform (EWT) is an adaptive signal decomposition method that inherits the advantages of EMD and WT methods, adaptively partitions the fourier spectrum to separate different modes by extracting frequency domain maxima, and then adaptively constructs a band pass filter bank in the frequency domain to construct orthogonal Wavelet functions to extract amplitude modulation-frequency modulation (AM-FM) components with tightly-supported fourier spectra. The EWT method can be divided into the following processes:
step 31: for a segment of time domain discrete electroencephalogram signal sequence x ∈ RN*1The Fourier spectrum F (x) is calculated and normalized to [0, π]；
Step 32: dividing the frequency spectrum according to a local maximum method, and taking the intermediate frequency between adjacent maximum points of the frequency spectrum as a boundary;
step 33: the mother wavelet of EWT is defined as the structure of Littlewood-Paley and Meyer wavelets used to design each interval LambdanLow pass and band pass filters on; the processed signal is one-dimensional EEG signal, Meyer wavelet is used, and its construction defines the partition interval LambdanThen adding wavelet window function, and constructing empirical scale function according to the divided frequency spectrum
And empirical wavelet function
In the above equations, ω is the frequency, ωkIs the k-th boundary frequency, γ is a conversion parameter used to ensure that there is no overlap between two consecutive frequencies, and there are many functions that satisfy this characteristic, which are commonly used:
β(x)＝x4(35-84x+70x2-20x3) (5)
step 34: after a set of tight supports is constructed, EWT is constructed according to the wavelet transform theory, and different modal components are obtained through a scale function and a wavelet function. Thus, detail coefficients and approximation coefficients of empirical wavelet transform can be obtained, and formulas are shown in formulas (6) and (7);
high frequency coefficient of detail
From the signal x and an empirical wavelet phinThe inner product of (t) yields:
approximationLow frequency coefficient
From the signal x and an empirical scale function
The inner product of (a) is obtained:
finally, inverse Fourier transform is applied to compute F (x) x ψ n (t) and
so that a time domain representation of each component can be obtained.
Because the electroencephalogram signals are random and non-stationary, if the Fourier spectrum of the electroencephalogram signals is directly divided by using a local maximum frequency spectrum division method, the division is unreasonable, and the problems of excessive or insufficient quantity exist. The problems of grid effect and frequency spectrum leakage are avoided when the time domain signal is cut off, on one hand, the grid effect is reduced by generally using a zero filling mode, so that the appearance of the frequency spectrum is smoother; on the other hand, there is a possibility that some spectral peaks that are difficult to confirm appear in the spectrum due to frequency domain leakage caused by data truncation, and in order to avoid loss of useful spectral peaks, useful peaks can be accurately found, and such a phenomenon can be eliminated after zero padding. Meanwhile, the interpolation in the time domain is easier to realize than the interpolation in the frequency domain, so the discovery provides the electroencephalogram signal frequency spectrum segmentation method based on the time domain interpolation and the frequency domain segmentation threshold selection.
In order to make the extreme point of the electroencephalogram signal clearer and improve the speed of searching the extreme point, interpolation operation is firstly carried out on the electroencephalogram signal, and meanwhile, in order to further determine the extreme point, a spectrum envelope line is adopted to replace an original spectrum to carry out extreme point selection. Compared with the original frequency spectrum, the envelope spectrum is more suitable for the non-stationarity of the electroencephalogram signal; and then, adaptively determining the amplitude threshold H according to an Otsu criterion, and finding a local extreme point and a corresponding lower label. And judging the local extreme value by using the amplitude threshold value, wherein subscripts corresponding to the extreme values larger than the threshold value are regarded as useful boundaries, and the corresponding frequency bands are regarded as effective frequency bands of the analyzed signals. The effective boundaries are counted to obtain the effective frequency band interval, so as to obtain the decomposition mode number Z, the process of which is shown in fig. 1.
Step 4, screening the essential characteristics of the original electroencephalogram signals and putting the essential characteristics into an intrinsic mode component set;
randomly selecting k samples from the eigenmode component set as a centroid, namely randomly initializing k atoms, performing dictionary learning by using a k-mean singular value decomposition method, and outputting a trained dictionary;
and 6, reconstructing the electroencephalogram signal at a reconstruction end by using the trained dictionary.
The EWT-KSVD dictionary learning method can adaptively learn a dictionary representing electroencephalogram characteristics. Firstly, EEWT decomposition is carried out on an original electroencephalogram signal; in order to reduce the time complexity of dictionary learning, relevance analysis is carried out on all the obtained intrinsic mode components, IMFs with small relevance are screened out, a K-SVD dictionary learning algorithm is used for learning, and a mode dictionary is learned. The overall framework of the specific algorithm is shown in fig. 2.
In order to verify the performance of the method provided by the invention, the provided EEWT-KSVD algorithm is comprehensively compared with the K-SVD algorithm. The experimental data of the invention adopts data in a multi-channel electroencephalogram signal motor imagery database eegmidb in a PhysioNet physiological signal database, 64-channel signals of 109 volunteers are collected by the data set, and each volunteer carries out 14 collection experiments. The sampling frequency is 256Hz, 64-channel electroencephalogram signals are denoised in EEGLAB, segmentation is carried out according to sampling points, the length of each segment is 256, normalization operation is carried out, then 70% of electroencephalogram data are used for training a dictionary, and the remaining 30% of electroencephalogram data are used as a test set for evaluating several dictionaries. In order to verify the performance of the proposed improved dictionary learning algorithm, the sparsity of dictionaries constructed by the two methods on coefficients expressed by signal sparsity and the effect of compressed sensing reconstruction are compared, and the sparsity index rho of a signal and Mean Square Error (MSE) before and after reconstruction are used as objective evaluation indexes for measuring the dictionaries.
To verify the EEWT performance in decomposing EEG, the EEG signal of a random segment shown in FIG. 3 is decomposed by using the EEWT, EEWT and the most common cubic spline interpolation envelope method in the frequency domain, FIG. 4 is a spectrum boundary segmentation graph, and the mode conditions decomposed by the three methods are shown in FIGS. 5-7.
The boundaries detected by the three methods are shown in fig. 4(a-c), where the dotted lines are the detected boundaries, indicating that the spectrum is divided into many parts. As can be seen from the spectrum segmentation graph, fig. 4(a) generates an invalid boundary when the position arrow directions of a and B indicate that the spectrum is divided, which will result in useless decomposition, i.e., unnecessary boundaries exist in the graph; fig. 4(b) only generates three boundaries, and the position C indicates that the closed frequency component cannot be divided, the frequency spectrum is not efficiently divided, and the required boundary is not detected; in fig. 4(c), the division point is mainly at the minimum point between the continuous maxima of the spectrum, and the reasonable spectrum division is obtained according to the scale space division principle of EWT.
Any signal is composed of the eigenmode components IMF, as can be seen from fig. 5-7, and the three methods decompose the signal into a different number of IMFs, each of which contains a component of the signal. IMF6 and IMF7 in FIG. 5 are very similar and present a problem of slight modal aliasing, resulting in a useless IMF; FIG. 6 does not completely separate the IMFs of the signals, resulting in too little IMF; relatively reasonable decomposition results are obtained in fig. 7. Meanwhile, the reconstruction error of EWT is 3.92e-6, the reconstruction error of cubic spline-EWT is 3.77e-6, the reconstruction error of EEWT is 3.46e-6, and the error of EEWT is slightly smaller than that of the other two methods. Thus, the EEWT performs better in resolving EEG. Experiments prove that when signals are interpolated, the effect of doubling is better than that of interpolation without interpolation and interpolation with triplex or quadruple interpolation, and under the condition of smaller error, long time is not consumed, so that the interpolation provided by the invention is doubled interpolation.
Since some fixed base dictionaries such as wavelet base and the like are not suitable for large-scale non-stationary electroencephalogram signal dictionaries, reconstruction errors are large, a large-scale overcomplete dictionary is mainly learned by using a K-SVD algorithm at present, dictionaries EMD-KSVD and EWT-KSVD learned based on the K-SVD algorithm and optimized dictionaries EEWT-KSVD learned by the K-SVD algorithm are learning dictionaries obtained by directly or indirectly training large-scale electroencephalogram signals, and the following four dictionary learning algorithms are mainly compared.
In the experiment, dictionaries with scales of 1024, 2048 and 4096 are respectively trained by using electroencephalogram signals of a training set, wherein sparse representation uses an orthogonal matching tracking algorithm, and atom updating uses an SVD decomposition algorithm. In order to measure and evaluate the sparsity of the four dictionaries, introducing sparsity indexes for comparison:
TABLE 1 dictionary sparsity index situation table of different scales
TABLE 2 sparse coefficient matrix sparse index case table for dictionaries of different scales
The table 1 is a sparse index condition table of dictionaries of different scales obtained by learning electroencephalogram signal data sets by four dictionary learning algorithms, and the table 2 is a sparse condition table of a sparse coefficient matrix when the dictionaries carry out sparse representation on electroencephalogram signals. As can be seen from Table 1, under different dictionary scales, the sparse index of the EEWT-KSVD learning dictionary is smaller than that of the other three learning dictionaries, the smaller the sparse index is, the stronger the sparse representation capability of the dictionary is represented, when the number of dictionary atoms is 1024, the sparse index of the K-SVD dictionary is the highest and has a value of 2.7063, but the sparse index of the EEWT-KSVD dictionary has a value of 1.5727, is reduced by 41.89% compared with the sparse index of the K-SVD, is reduced by 31.01% compared with the sparse index of the EMD-KSVD, is reduced by 20.16% compared with the sparse index of the EWT-KSVD, and the dictionary sparse effect is more obvious. In table 2, the sparse coefficient matrix sparsity index of the EEWT-KSVD dictionary for sparse representation of signals is the lowest, so that the sparse representation capability of the EEWT-KSVD is better when the sparse index is used as a measure data index for learning dictionary sparsity.
In order to further verify the effectiveness of the EEWT-KSVD method, the dictionaries learned by the four methods are evaluated for accuracy under different compression ratios (0.1, 0.2, 0.3, 0.4, 0.5, respectively) and dictionary scales, and the results of comparing the mean square errors of the signals before and after reconstruction are shown in table 3.
TABLE 3 dictionary learning algorithm mean square error situation table under different compression ratios
From table 3, it is seen that, the dictionaries obtained by using different dictionary learning methods perform sparse representation and reconstruction on signals, and generally, under the condition that the atomic scale of the dictionaries is the same, the larger the compression ratio is, the smaller the reconstruction error is, and as the compression ratio is increased, that is, the number of measured values is increased, the more the number of electroencephalogram signals acquired under the same condition is, the smaller the error is; under the condition that the compression ratio is the same, the larger the atomic scale of the dictionary is, the larger the number of non-zero values in the signal sparse representation coefficient is, and the smaller the reconstruction error is. But the errors of the EEWT-KSVD are smaller, i.e. the reconstruction accuracy is higher, than the errors of several other methods. For example, when the compression ratio is 0.3 and the number of dictionary atoms is 1024, the EEWT-KSVD has a higher practicability because the error is reduced by 9.70% compared with the EMD-KSVD, by 5.41% compared with the EWT-KSVD, and by 21.71% compared with the K-SVD.
In order to more intuitively see the reconstruction effect of four different learning dictionaries on electroencephalogram signal compression sensing, when the compression ratio is 0.5, a section of signal is randomly selected, and the ratio of the reconstruction of the section of signal by using the different dictionaries is shown in fig. 8.
Therefore, the improved empirical wavelet transform dictionary learning algorithm provided by the invention is superior to the original KSVD, EMD-KSVD and EWT-KSVD dictionary learning algorithms, and has certain advantages for the sparse representation problem of the electroencephalogram signals.
The method is based on sparse indexes and reconstructed root mean square error indexes, a brain electrical signal dictionary learning model is established, and meanwhile empirical wavelet transformation is improved to obtain more reasonable modal segmentation. Simulation results show that the dictionary learning method researched by the invention is reasonable, effective and easy to realize, fully utilizes the self characteristics of signals, and has higher sparsity and reconstruction accuracy.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.
Claims (3)
1. The electroencephalogram signal dictionary learning method based on improved experience wavelet transform is characterized by comprising the following steps:
acquiring an electroencephalogram signal data set;
dividing signals in the electroencephalogram signal data set into electroencephalogram signal segments with the same length;
dividing the electroencephalogram signal fragments into a plurality of intrinsic mode components by using an improved empirical wavelet transform mode, wherein the intrinsic mode components can reflect the essential characteristics of the original electroencephalogram signals;
screening the essential characteristics of the original electroencephalogram signals and putting the essential characteristics into an intrinsic mode component set;
randomly selecting k samples from the eigenmode component set as a centroid, namely randomly initializing k atoms, performing dictionary learning by using a k-mean singular value decomposition method, and outputting a trained dictionary;
and reconstructing the electroencephalogram signal at a reconstruction end by using the trained dictionary.
2. The electroencephalogram signal dictionary learning method based on the improved empirical wavelet transform, according to claim 1, wherein the improved empirical wavelet transform mode specifically is:
performing interpolation operation on the electroencephalogram signals, and selecting extreme points by adopting a spectrum envelope curve;
adaptively determining an amplitude threshold value H according to an Otsu criterion;
judging the local extremum by using the amplitude threshold H, wherein subscripts corresponding to extremums larger than the amplitude threshold are regarded as useful boundaries, and corresponding frequency bands are regarded as effective frequency bands of the analyzed electroencephalogram signals;
and counting the useful boundaries to obtain an effective frequency band interval and obtain a decomposition modal number Z.
3. The electroencephalogram signal dictionary learning method based on the improved experience wavelet transform as recited in claim 1, wherein the feature of the original electroencephalogram signal essence is screened, and specifically: obtaining a correlation coefficient between each intrinsic mode component and other intrinsic mode components by using the following formula, then obtaining an average correlation coefficient of each intrinsic mode component and normalizing to [0,1], setting the absolute value of the correlation coefficient to be less than 0.5 as weak correlation, and selecting a mode with the correlation degree of less than 0.5;
in the above formula, Cov (x)i,xj) Represents the covariance of the ith and jth modes, Var [ x ]i]And Var [ x ]j]The variance of the eigenmode components of the ith and j empirical wavelet decompositions is respectively represented.
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