CN110269609B - Method for separating ocular artifacts from electroencephalogram signals based on single channel - Google Patents

Method for separating ocular artifacts from electroencephalogram signals based on single channel Download PDF

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CN110269609B
CN110269609B CN201910609879.2A CN201910609879A CN110269609B CN 110269609 B CN110269609 B CN 110269609B CN 201910609879 A CN201910609879 A CN 201910609879A CN 110269609 B CN110269609 B CN 110269609B
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electroencephalogram
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吴全玉
张文强
张文悉
吴志斌
李姝�
陶为戈
潘玲佼
王烨
刘晓杰
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Changzhou Digital Intelligence Adaptive Technology Center (L.P.)
Jiangsu Tianyu Technology Co ltd
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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/24—Detecting, measuring or recording bioelectric or biomagnetic signals of the body or parts thereof
    • A61B5/316—Modalities, i.e. specific diagnostic methods
    • A61B5/369—Electroencephalography [EEG]
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7203—Signal processing specially adapted for physiological signals or for diagnostic purposes for noise prevention, reduction or removal
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235—Details of waveform analysis
    • A61B5/725—Details of waveform analysis using specific filters therefor, e.g. Kalman or adaptive filters

Abstract

The invention discloses a method for separating ocular artifacts from electroencephalogram signals based on a single channel, which comprises the following steps: s1, carrying out self-adaptive noise complete empirical mode decomposition on the electroencephalogram signal to be separated acquired in a single channel to obtain n modal components as observation signals, wherein the electroencephalogram signal is mixed with ocular artifacts; s2, converting the convolution mixed model of the observation signal into an instantaneous mixed model x (t) As (t), wherein the observation signal is formed by convolution mixing of 2-dimensional source signals; s3, establishing a cost function J (W) according to a joint block diagonalization principle and an observation signal converted into an instantaneous mixed model based on mutual independence between an ocular artifact and a pure electroencephalogram signal in the electroencephalogram signal; s4, carrying out iterative optimization on the cost function J (W) according to a conjugate gradient method to obtain an estimation value of an inverse matrix W
Figure DDA0003187291720000011
S5 estimation value based on inverse matrix W
Figure DDA0003187291720000012
Calculating to obtain pure electroencephalogram signals
Figure DDA0003187291720000013
The method has the advantages that the eye electrical artifact in the electroencephalogram signal is separated by adopting a blind deconvolution separation method, so that the separation precision is greatly improved, and the accurate and pure electroencephalogram signal is obtained.

Description

Method for separating ocular artifacts from electroencephalogram signals based on single channel
Technical Field
The invention relates to the technical field of signal processing, in particular to a method for separating ocular artifacts in electroencephalogram signals.
Background
The brain of a person contains a lot of important information, people also continuously research the brain, and the research on the brain electrical signals is always the key point of the brain research because the brain electrical signals contain a lot of brain information.
Because the electroencephalogram signals have the characteristics of strong randomness, strong non-stationarity, nonlinearity, weak signals, strong noise interference and the like, the acquisition of the electroencephalogram signals can be influenced by external stimulation, physiological condition change, medicine influence and the like. In addition, microvolt (μ V) level electroencephalogram signals are also easily interfered by eye movement (EOG), Electromyogram (EMG), Electrocardiogram (ECG) and the like, so that the electroencephalogram signals cannot be accurately expressed by a mathematical formula, and the acquired electroencephalogram signals are also easily interfered by additional noises such as ocular artifacts, electromyogram artifacts and the like introduced by acquisition equipment and the like, so that the authenticity of the electroencephalogram signals is seriously influenced, and the analysis and the processing of the electroencephalogram signals become very complicated. Especially for the analysis of single-channel electroencephalogram signals, because of the lack of reference electro-ocular signals and low precision, the artifact removal is difficult.
At present, a plurality of achievements are obtained for the research of methods for removing ocular artifacts in electroencephalogram signals, but most of the methods aim at removing ocular artifacts of multi-channel electroencephalogram signals. The method comprises the steps of applying a plurality of methods such as Principal Component Analysis (PCA), Independent Component Analysis (ICA) and the like, wherein the principal component analysis method analyzes principal components in signals by comparing electroencephalogram signals and ocular electric signals which are recorded simultaneously, and removes ocular artifacts after judging the ocular artifacts; the independent component analysis is to assume that each original signal S is mutually independent, and the original signal S and the matrix A are calculated to obtain an observation signal X, namely an observation signal containing ocular artifacts, which is acquired by an electroencephalogram sensor; then, the independent components are separated from the observation signals by selecting a proper objective function and solving a separation matrix W. However, both principal component analysis and independent component analysis methods have the problem of component selection, need to be manually judged, have high precision requirements and need more electroencephalogram data channels.
In the research of removing ocular artifacts in single-channel electroencephalogram signals. At first, people use a soft and hard threshold method to search and remove ocular artifacts, but when the amplitude of the ocular artifacts is close to that of the electroencephalogram signals, effective information in the electroencephalogram signals is filtered out. And then, an ocular artifact separation method based on wavelet transformation and Ensemble Empirical Mode Decomposition (EEMD) is provided, the electroencephalogram signals are decomposed into a plurality of groups of electroencephalogram signal data through methods such as wavelet transformation and ensemble empirical mode decomposition, and the threshold value for filtering the ocular artifacts is determined through discrimination methods such as fuzzy entropy, approximate entropy and a big-Massart strategy. However, the selection of wavelet base in the wavelet transformation method needs human intervention and does not meet the self-adaptive requirement; the empirical mode decomposition method easily causes mode aliasing and influences the accuracy of judging the ocular artifacts.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for separating ocular artifacts from an electroencephalogram signal based on a single channel, which effectively solves the problem that the accuracy of the electroencephalogram signal is low due to large ocular artifact noise in the electroencephalogram signal acquired by the single channel.
In order to achieve the purpose, the invention is realized by the following technical scheme:
a method for separating ocular artifacts from electroencephalogram signals based on a single channel comprises the following steps:
s1, carrying out self-adaptive noise complete empirical mode decomposition on the electroencephalogram signal to be separated acquired in a single channel to obtain n modal components as observation signals, wherein the electroencephalogram signal is mixed with ocular artifacts;
s2, converting the convolution mixture model of the observation signal into an instantaneous mixture model x (t) as (t), where the observation signal is formed by convolution mixing of 2-dimensional source signals;
wherein t is the sampling time point of the electroencephalogram signal, and n-dimensional observation signal x (t) ═ x1(t)，x2(t)，...，xK(t)]M dimensional source signal
Figure GDA0003187291710000021
The mixing matrix A ═ Aij)，
Figure GDA0003187291710000022
hijThe convolution mixing process from the jth source signal to the ith observation point is represented by an FIR filter, i is 1, 2, …, K, j is 1, 2, …, m, l represents the order of the filter;
s3, establishing a cost function J (W) according to a joint block diagonalization principle and an observation signal converted into an instantaneous mixed model based on mutual independence between an ocular artifact and a pure electroencephalogram signal in the electroencephalogram signal;
Figure GDA0003187291710000023
wherein | · | purple sweetFThe Frobenius norm of the matrix is represented, offbdiag represents the off-diagonal block portion of the matrix, and W represents the inverse of the mixing matrix a; tau isqDenotes time delay, Q ═ 1, 2, …, Q; wHA conjugate transpose matrix representing W; rx(τq) Representing the observed signal x (t) at a time delay τqAutocorrelation matrix of, and Rx(τq)＝ARs(τq)AH，AHA conjugate transpose matrix representing the mixing matrix a;
s4, carrying out iterative optimization on the cost function J (W) according to a conjugate gradient method to obtain an estimation value of an inverse matrix W
Figure GDA0003187291710000031
S5 estimation value based on inverse matrix W
Figure GDA0003187291710000032
Calculating to obtain pure electroencephalogram signals
Figure GDA0003187291710000033
The eye electrical artifact can be separated from the electroencephalogram signal.
The method for separating the ocular artifacts from the electroencephalogram signals based on the single channel adopts a self-adaptive noise-complete empirical mode decomposition (CEEMDAN) method to decompose the electroencephalogram signals acquired by the single-channel electroencephalogram signal sensor into multi-dimensional signal data (namely observation signals of the electroencephalogram signals), so that the ocular artifacts can be more easily distinguished from the electroencephalogram signals. When the ocular artifacts of the multidimensional electroencephalogram signal data decomposed by the CEEMDAN are separated, the description method of the convolution mixed model is adopted to be more consistent with the propagation model of the electroencephalogram signal in consideration of the multi-directionality and the time delay of the transmission of the electroencephalogram signal, so that the ocular artifacts in the electroencephalogram signal are separated by adopting the separation method of blind deconvolution, the separation precision is greatly improved, and the accurate and pure electroencephalogram signal is obtained.
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A more complete understanding of the present invention, and the attendant advantages and features thereof, will be more readily understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein:
FIG. 1 is a flow chart of a method for separating ocular artifacts from multi-electroencephalogram signals according to the present invention;
FIG. 2 is a diagram of the original electroencephalogram signal in the present invention;
FIG. 3 is a time domain diagram of a plurality of modal components obtained by subjecting Fp1 channel 10s electroencephalogram signals to CEEMDAN decomposition;
FIG. 4 is a graph comparing a separated electroencephalogram signal with a separated noise in the present invention;
FIG. 5 is a contrast diagram of the original EEG signal and the EEG signal after the eye artifacts are separated.
Detailed Description
In order to make the contents of the present invention more comprehensible, the present invention is further described below with reference to the accompanying drawings. The invention is of course not limited to this particular embodiment, and general alternatives known to those skilled in the art are also covered by the scope of the invention.
Aiming at the problem that the accuracy of an electroencephalogram signal is not high due to high eye artifact noise in the electroencephalogram signal acquired by a single channel, the invention provides a method for separating the eye artifact in the electroencephalogram signal based on the single channel, as shown in figure 1, the method for separating the eye artifact in the electroencephalogram signal comprises the following steps:
s1, CEEMDAN decomposition is carried out on the electroencephalogram signal to be separated acquired by a single channel, n modal components are obtained to be used as observation signals, and ocular artifacts are mixed in the electroencephalogram signal;
s2, converting the convolution mixed model of the observation signal into an instantaneous mixed model x (t) As (t), wherein the observation signal is formed by convolution mixing of 2-dimensional source signals;
wherein t is the sampling time point of the electroencephalogram signal, and the K-dimensional observation signal x (t) ═ x1(t)，x2(t)，...，xK(t)]M dimensional source signal
Figure GDA0003187291710000041
The mixing matrix A ═ Aij)，
Figure GDA0003187291710000042
hijThe convolution mixing process from the jth source signal to the ith observation point is represented by an FIR filter, i is 1, 2, …, K, j is 1, 2, …, m, l represents the order of the filter;
s3, establishing a cost function J (W) according to a joint block diagonalization principle and an observation signal converted into an instantaneous mixed model based on mutual independence between an ocular artifact and a pure electroencephalogram signal in the electroencephalogram signal;
Figure GDA0003187291710000043
wherein | · | purple sweetFThe Frobenius norm of the matrix is represented, offbdiag represents the off-diagonal block portion of the matrix, and W represents the inverse of the mixing matrix a; tau isqDenotes time delay, Q ═ 1, 2, …, Q; wHTo representA conjugate transpose matrix of W; rx(τq) Representing the observed signal x (t) at a time delay τqAutocorrelation matrix of, and Rx(τq)＝ARS(τq)AH，AHA conjugate transpose matrix representing the mixing matrix a;
s4, carrying out iterative optimization on the cost function J (W) according to a conjugate gradient method to obtain an estimation value of an inverse matrix W
Figure GDA0003187291710000044
S5 estimation value based on inverse matrix W
Figure GDA0003187291710000045
Calculating to obtain pure electroencephalogram signals
Figure GDA0003187291710000046
The eye electrical artifact can be separated from the electroencephalogram signal.
In the method for separating the ocular artifacts from the electroencephalogram signals, the observation signals are specifically electroencephalogram signals directly collected by an electroencephalogram signal sensor, and the signals are mixed with ocular signals to serve as noise to influence the accuracy of the electroencephalogram signals; the source signals are separate electroencephalogram signals and separate electrooculogram signals, the algorithm processes the collected observation signals and separates the electroencephalogram signals and the electrooculogram signals, and the pure electroencephalogram signals are separated electroencephalogram signals.
In step S3, the autocorrelation matrix Rx(τq) The derivation is as follows:
since the source signals s (t) are independent of each other and the same source signal is correlated at different time delays τ, the autocorrelation matrix R of the source signals s (t)S(τ) is the block diagonal matrix:
Figure GDA0003187291710000051
wherein the content of the first and second substances,
Figure GDA0003187291710000052
from the autocorrelation matrix R of the source signal s (t)S(τ) autocorrelation of x (t) as (t) can be obtained:
Rx(τ)＝ARS(τ)AH
for the time delay tau, take a plurality of time delays tauqQ is 1, 2, …, Q, given by:
Rx(τq)＝ARS(τq)AH。
the method for separating the ocular artifacts in the electroencephalogram signal is further explained by an example as follows:
taking electroencephalogram signals in a CHB-MIT scalp electroencephalogram database in a PhysioNet database as a data source, selecting 10s electroencephalogram signals collected at an electrode Fp1 close to eyes (the sampling frequency is 256Hz, the reference electrode is a left earlobe) for carrying out eye electrical artifact separation, and obtaining an original electroencephalogram signal containing eye electrical artifacts as shown in figure 2, wherein the abscissa is a sampling point and the ordinate is an amplitude (mu V).
After the electroencephalogram signal is collected, step S1 is immediately performed, CEEMDAN decomposition is performed on the electroencephalogram signal, and n modal components are obtained as observation signals, specifically:
s11 adding white Gaussian noise to the observed signal to obtain a constructed signal xj(t)＝x(t)+σ0wj(t), where x (t) is the observed signal, σ0To find the noise standard deviation, w, of the 1 st modal componentj(t) is white noise that follows an N (0, 1) distribution, and j is 1, 2, …, N. In this example, the noise standard deviation σ is selected00.2 and 100. In the process, white noise is added into the observed signal by utilizing the characteristic of white noise frequency uniform distribution, so that the constructed signal xiAnd (n) the extreme points are uniformly distributed in the whole frequency band at intervals and have continuity on different scales, so that the modal aliasing effect is reduced.
S12 pairs of construction signals xj(t) performing EMD for N times to obtain N first-order components, and averaging the components to obtain a first modal component
Figure GDA0003187291710000053
And a firstA residual signal r1(t)：
Figure GDA0003187291710000061
Figure GDA0003187291710000062
S13 judging residual signal r1(t) determining whether the number of extreme points exceeds two, and if so, adding a first-order residual signal r to a first-order modal operator decomposed by EMD1(t) the constituent signal r1(t)+σ1M1[wj(t)]EMD decomposition is carried out to obtain a second modal component
Figure GDA0003187291710000063
Figure GDA0003187291710000064
Wherein σ1Representing the standard deviation of the noise in the calculation of the 2 nd modal component, Ma[·]Defined as the operator of the a-th IMF mode after EMD decomposition of the signal, M1[wj(t)]Operator of the first modality, w, generated for EMD decompositionj(t) represents white gaussian noise added by the j-th decomposition;
s14 is executed by looping step S13 until the number of extreme points of the residual signal obtained by the previous layer of modal decomposition is judged to be not more than two, and decomposition is stopped to obtain a final residual signal r (t):
Figure GDA0003187291710000065
wherein K represents the number of modal decompositions; k represents the number of layers of modal decomposition, K is 1, 2, …, K;
the original signal x (t) is decomposed into:
Figure GDA0003187291710000066
decomposing at the k layer, and calculating the k residual signal rk(t) and (k + 1) th modal component
Figure GDA0003187291710000067
Figure GDA0003187291710000068
Figure GDA0003187291710000069
Wherein the content of the first and second substances,
Figure GDA00031872917100000610
representing the k-th modal component, σkThe noise standard deviation when the (k + 1) th modal component is found is shown.
Fig. 3 is a time domain diagram of a plurality of modal components obtained by decomposing the Fp1 channel 10s electroencephalogram signal through CEEMDAN in this example, where the abscissa is a sample point and the ordinate is a corresponding modal component.
More specifically, in this process, EMD is decomposed into:
s01, finding out the local extreme point of the observation signal x (t), forming a lower envelope (int) (t) for the local extreme point by using an interpolation method, and forming an upper envelope emax (t) for the local extreme value;
s02 calculates a mean value according to the formula m (t) ═ (emint (t) + emax (t))/2, and further calculates: the difference d (t) x (t) -m (t);
s03, if the difference d (t) meets the requirement of the preset IMF function, taking the difference d (t) as the modal component of the decomposition; if not, the difference d (t) is repeated to observe the signals x (t) in the steps S01 and S02, and iteration is carried out until the difference d (t) meets the IMF function requirement, and modal components are output. The IMF function requirements are: in the whole time range, the number of the local extreme points is equal to or different from that of the zero-crossing points by one; and at any time point, the average value of the envelope of the local maximum value and the envelope of the local minimum value is zero.
After CEEMDAN decomposition is performed on the acquired electroencephalogram signal, the process proceeds to step S2, where a convolution mixture model of the observation signal is converted into an instantaneous mixture model x (t) as (t), where the 12-dimensional observation signal is formed by convolution mixing of 2-dimensional source signals.
Specifically, observed Signal xiThe convolution mixture model of (a) is:
Figure GDA0003187291710000071
where l denotes the order of the filter, p ═ 1, 2, …, (l-1). In this example, the order of the filter is set to 2, the time window length w is taken to be 6, and the filter coefficients are randomly generated, specifically: h ═ Hij)12×2Wherein H isij＝aij+bijz-1Wherein a isijAnd bijThe coefficients are generated randomly.
Setting a time window with the length of w and satisfying Kw ≥ m (w + l-1), observing signal x at time ti(t) is:
xi(t)＝[xi(t)，xi(t-1)，...xi(t-w+1)]T
writing in vector form yields:
Figure GDA0003187291710000081
therefore, the convolution mixture model can be written as x (t) ═ as (t), and the conversion from the electroencephalogram signal mixture model to the transient mixture model is completed.
Then step S3 is entered, because the ocular artifacts in the EEG signal and the pure EEG signal are independent, the source signals are also independent, the autocorrelation matrix R of the source signal S (t)S(τ) is the block diagonal matrix:
Figure GDA0003187291710000082
where τ is the time delay, H represents the conjugate transpose of s (t- τ),
Figure GDA0003187291710000083
calculating an autocorrelation matrix R for the observed signals x (t) as (t)x(τ)：
Rx(τ)＝ARS(τ)AH
Using the inverse matrix W for representation:
WRx(τ)WH＝RS(τ)
based on this, a number of time delays τ are taken according to the joint block diagonalization principleqQ is 1, 2, …, Q (in this example, Q is 20), and a plurality of R is obtainedx(τq) And establishing a cost function J (W) such that WRx(τq)WHThe off-diagonal block portion of (a) approaches zero:
Figure GDA0003187291710000084
wherein | · | purple sweetFThe Frobenius norm of the matrix is denoted and the offbdiag denotes the off-diagonal block portion of the matrix.
Then, step S4 is performed, iterative optimization is performed on the cost function J (W) according to the conjugate gradient method, and the estimation value of the inverse matrix W is obtained
Figure GDA0003187291710000085
The iteration process specifically comprises the following steps:
autocorrelation matrix R of S41 for time delay τ equal to 0x(0) Decomposing the characteristic value to obtain Rx(0)＝VDVHWherein V is an eigenvector matrix, and D is an eigenvalue matrix; arranging the eigenvalues in the eigenvalue matrix D according to a descending order to construct a whitening matrix
Figure GDA0003187291710000086
Then whitening processing is carried out on the observation signal according to the whitening matrix;
s42 sets initial value W of inverse matrix W0Normalizing the initial value to give a termination threshold value epsilon of 0.01, and enabling the initial value k to be 0;
s43 is based on the formula
Figure GDA0003187291710000091
Computing
Figure GDA0003187291710000092
And let d have a value of0＝-g0；
S44 is based on formula Wk+1＝Wk+αkdkCalculating Wk+1And performing standardization Wk+1＝Wk+1/||Wk+1||FWherein α iskIs a step size factor, generated by a strong Wolfe linear search method;
s45 judges | Wk+1-Wk||If F is less than or equal to epsilon, stopping iteration and outputting
Figure GDA0003187291710000093
S46 order ndimDimension of inverse matrix W, if k ═ ndimThen k +1, W0＝Wk+1And jumps to step S43; and then calculate gk+1And dk+1Wherein, in the step (A),
Figure GDA0003187291710000094
dk+1＝-gk+1+βkdkthen, the process proceeds to step S44.
Obtaining an estimated value of an inverse matrix W
Figure GDA0003187291710000095
Then, pure brain electrical signals are obtained through calculation
Figure GDA0003187291710000096
The separation of the ocular artifacts from the electroencephalogram signals is realized, and the separated electroencephalogram signals and the separated noise are shown in fig. 4, wherein fig. 4(a) is a separated electroencephalogram signal diagram, fig. 4(b) is a separated noise diagram, and the ocular artifacts can be obviously removed from the diagram. Fig. 5 is a comparison graph of an original electroencephalogram signal and an ocular artifact after separation, wherein fig. 5(a) is an original electroencephalogram signal graph, and fig. 5(b) is an electroencephalogram signal graph after the ocular artifact is separated, so that the detailed information in the original electroencephalogram signal can be well reserved.

Claims (8)

1. A method for separating ocular artifacts from electroencephalogram signals based on a single channel is characterized by comprising the following steps:
s1, carrying out self-adaptive noise complete empirical mode decomposition on the electroencephalogram signal to be separated acquired in a single channel to obtain n modal components as observation signals, wherein the electroencephalogram signal is mixed with ocular artifacts;
s2, converting the convolution mixture model of the observation signal into an instantaneous mixture model x (t) as (t), where the observation signal is formed by convolution mixing of 2-dimensional source signals;
wherein t is the sampling time point of the electroencephalogram signal, and n-dimensional observation signal x (t) ═ x1(t)，x2(t)，...，xK(t)]M dimensional source signal
Figure FDA0003187291700000011
The mixing matrix A ═ Aij)，
Figure FDA0003187291700000012
hijThe convolution mixing process from the jth source signal to the ith observation point is represented by an FIR filter, i is 1, 2, …, K, j is 1, 2, …, m, l represents the order of the filter;
s3, establishing a cost function J (W) according to a joint block diagonalization principle and an observation signal converted into an instantaneous mixed model based on mutual independence between an ocular artifact and a pure electroencephalogram signal in the electroencephalogram signal;
Figure FDA0003187291700000013
wherein | · | purple sweetFThe Frobenius norm of the matrix is represented, offbdiag represents the off-diagonal block portion of the matrix, and W represents the inverse of the mixing matrix a; tau isqDenotes time delay, Q ═ 1, 2, …, Q; wHA conjugate transpose matrix representing W; rx(τq) Representing the observed signal x (t) at a time delay τqAutocorrelation matrix of, and Rx(τq)＝ARs(τq)AH，AHA conjugate transpose matrix representing the mixing matrix a;
s4, carrying out iterative optimization on the cost function J (W) according to a conjugate gradient method to obtain an estimation value of an inverse matrix W
Figure FDA0003187291700000014
S5 estimation value based on inverse matrix W
Figure FDA0003187291700000015
Calculating to obtain pure electroencephalogram signals
Figure FDA0003187291700000016
The eye electrical artifact can be separated from the electroencephalogram signal.
2. The method for separating ocular artifacts from electroencephalogram signals according to claim 1, characterized in that in step S1 includes:
s11 adding white Gaussian noise to the observed signal to obtain a constructed signal xj(t)＝x(t)+σ0wj(t), where x (t) is the observed signal, σ0To find the noise standard deviation, w, of the 1 st modal componentj(t) is white noise that follows an N (0, 1) distribution, j ═ 1, 2, …, N;
s12 pairs of construction signals xj(t) performing EMD for N times to obtain N first-order components, and averaging the components to obtain a first modal component
Figure FDA0003187291700000021
And a first residual signal r1(t)：
Figure FDA0003187291700000022
Figure FDA0003187291700000023
S13 judging residual signal r1(t) determining whether the number of extreme points exceeds two, and if so, adding a first-order residual signal r to a first-order modal operator decomposed by EMD1(t) the constituent signal r1(t)+σ1M1[wj(t)]EMD decomposition is carried out to obtain a second modal component
Figure FDA0003187291700000024
Figure FDA0003187291700000025
Wherein σ1Representing the standard deviation of the noise in the calculation of the 2 nd modal component, Ma[·]Defined as the operator of the a-th IMF mode after EMD decomposition of the signal, M1[wj(t)]Operator of the first modality, w, generated for EMD decompositionj(t) represents white gaussian noise added by the j-th decomposition;
s14 is executed by looping step S13 until the number of extreme points of the residual signal obtained by the previous layer of modal decomposition is judged to be not more than two, and decomposition is stopped to obtain a final residual signal r (t):
Figure FDA0003187291700000026
wherein K represents the number of modal decompositions; k represents the number of layers of modal decomposition, K is 1, 2, …, K;
the original signal x (t) is decomposed into:
Figure FDA0003187291700000027
decomposing at the k layer, and calculating the k residual signal rk(t) and (k + 1) th modal component
Figure FDA0003187291700000031
Figure FDA0003187291700000032
Figure FDA0003187291700000033
Wherein the content of the first and second substances,
Figure FDA0003187291700000034
representing the k-th modal component, σkThe noise standard deviation when the (k + 1) th modal component is found is shown.
3. The method for separating ocular artifacts from electroencephalogram signals of claim 2, wherein the EMD is decomposed into:
s01, finding out the local extreme point of the observation signal x (t), forming a lower envelope (int) (t) for the local extreme point by using an interpolation method, and forming an upper envelope emax (t) for the local extreme value;
s02 calculates a mean value according to the formula m (t) ═ (emint (t) + emax (t))/2, and further calculates: the difference d (t) x (t) -m (t);
s03, if the difference d (t) meets the requirement of the preset IMF function, taking the difference d (t) as the modal component of the decomposition; if not, the difference d (t) is repeated to observe the signals x (t) in the steps S01 and S02, and iteration is carried out until the difference d (t) meets the IMF function requirement, and modal components are output.
4. The method for separating ocular artifacts from electroencephalogram signals according to claim 3, wherein in step S03, the IMF function requirements are: in the whole time range, the number of the local extreme points is equal to or different from that of the zero-crossing points by one; and at any time point, the average value of the envelope of the local maximum value and the envelope of the local minimum value is zero.
5. The method for separating ocular artifacts from brain electrical signals according to claim 1, 2 or 3, characterized in that in step S2:
observed Signal xiThe convolution mixture model of (t) is:
Figure FDA0003187291700000035
wherein l denotes the order of the filter, p ═ 1, 2, …, (l-1);
setting a time window with the length of w, and satisfying that Kw is more than or equal to m (w + l-1), observing the signal x of the electroencephalogram signal at the time ti(t) is:
xi(t)＝[xi(t)，xi(t-1)，...xi(t-w+1)]T
writing in vector form yields:
Figure FDA0003187291700000041
therefore, the convolution mixture model can be written as x (t) ═ as (t), and the conversion from the electroencephalogram signal mixture model to the transient mixture model is completed.
6. The method of separating ocular artifacts from electroencephalogram signals of claim 5, whereinIn step S3, the autocorrelation matrix R of the source signal S (t)S(τ) is the block diagonal matrix:
Figure FDA0003187291700000042
wherein tau is time delay, H represents a conjugate transpose matrix shown as s (t-tau),
Figure FDA0003187291700000043
autocorrelation matrix R of observed signals x (t) as (t)x(τ) is:
Rx(τ)＝ARS(τ)AH
the inverse matrix is used for representation:
WRx(τ)WH＝RS(τ)
taking a plurality of time delays tau according to the principle of joint block diagonalizationqQ is 1, 2, …, Q, and a plurality of R is obtainedx(τq)；
Establishing a cost function J (W) such that WRx(τq)WHThe off-diagonal block portion of (a) approaches zero:
Figure FDA0003187291700000044
wherein | · | purple sweetFThe Frobenius norm of the matrix is denoted and the offbdiag denotes the off-diagonal block portion of the matrix.
7. The method for separating ocular artifacts from electroencephalogram signals of claim 6, wherein in the conjugate gradient method of step S4, the iterative formula is:
Wk+1＝Wk+αkdk
Figure FDA0003187291700000045
dk+1＝-gk+1+βkdk
wherein alpha iskIs a step size factor, generated by a strong Wolfe linear search method; dkAnd betakGiven d0Is iteratively obtained d0＝-g0；gkThe calculation formula is as follows:
Figure FDA0003187291700000051
。
8. the method for separating ocular artifacts from brain electrical signals according to claim 7, wherein, in step S4,
autocorrelation matrix R of S41 for time delay τ equal to 0x(0) Decomposing the characteristic value to obtain Rx(0)＝VDVHWherein V is an eigenvector matrix, and D is an eigenvalue matrix; arranging the eigenvalues in the eigenvalue matrix D according to a descending order to construct a whitening matrix
Figure FDA0003187291700000052
Then whitening the observation signal x (t) according to the whitening matrix;
s42 sets initial value W of inverse matrix W0Normalizing the initial value, giving a termination threshold value epsilon > 0, and enabling k to be 0;
s43 calculation
Figure FDA0003187291700000053
And let d have a value of0＝-g0；
S44 calculating W according to the iteration formula of the inverse matrix Wk+1And performing standardization Wk+1＝Wk+1/||Wk+1||F；
S45 judges | Wk+1-Wk||FIf the epsilon is not more than epsilon, stopping iteration and outputting
Figure FDA0003187291700000054
S46 order ndimDimension of inverse matrix W, if k ═ ndimLet k equal to k +1, W0＝Wk+1And jumps to step S43; respectively calculate gk+1And dk+1Then, the process proceeds to step S44.
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