CN112494043B - Electroencephalogram signal detection method based on tensor method - Google Patents

Electroencephalogram signal detection method based on tensor method Download PDF

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CN112494043B
CN112494043B CN202011261249.XA CN202011261249A CN112494043B CN 112494043 B CN112494043 B CN 112494043B CN 202011261249 A CN202011261249 A CN 202011261249A CN 112494043 B CN112494043 B CN 112494043B
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matrix
electroencephalogram
psychological
signal
tester
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CN112494043A (en
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韩曦
刘芹
姚敏
郑争
王瑞伟
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North China University of Technology
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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
    • A61B5/16—Devices for psychotechnics; Testing reaction times ; Devices for evaluating the psychological state
    • A61B5/165—Evaluating the state of mind, e.g. depression, anxiety
    • 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
    • A61B5/7253—Details of waveform analysis characterised by using transforms
    • A61B5/7257—Details of waveform analysis characterised by using transforms using Fourier transforms

Abstract

The invention discloses an electroencephalogram signal detection method based on a tensor method, which comprises the following steps of: step1, establishing a PARAFAC model based on the acquired electroencephalogram signals; step2, extracting the psychological parameter characteristics of the electroencephalogram signals by adopting an alternative least square method to obtain a psychological parameter matrix, an electroencephalogram tester channel characteristic matrix and an acquisition environment matrix; step3, performing identifiability condition analysis on the characteristics of the physiological parameters through the uniqueness of the PARAFAC model; and 4, performing fast Fourier transform on a psychological generation mechanism and a psychological abnormal factor parameter of the electroencephalogram signal psychological parameter matrix to obtain an amplitude-frequency characteristic curve of the psychological parameter for later psychological diagnosis and treatment. The tensor has a research space in the expression and analysis of high-dimensional data, and the internal structure of some data cannot be damaged; the psychological characteristic parameters of the electroencephalogram signals are accurately detected and extracted.

Description

Electroencephalogram signal detection method based on tensor method
Technical Field
The invention belongs to the technical field of electroencephalogram signal detection, and particularly relates to an electroencephalogram signal detection method based on a tensor method.
Background
With the development of information science and technology, the idea that a heavenly horse in the brain of some people runs empty is slowly becoming a reality. Among them, electroencephalogram has been gradually applied to real life, and electroencephalogram is a signal generated by brain neuron activity, and contains abundant brain state information and a large amount of physiological information related to human body, and electroencephalogram information is receiving more and more attention from people. Research shows that the electroencephalogram signals with different psychological changes are different, and when the mind or emotion changes, the electroencephalogram signal components related to the psychology also change, and the psychological changes of patients with psychological disorders can be observed by reading the electroencephalogram signals.
In the conventional method, data is generally represented in a matrix form, and even if the original data is a high-order structure, the original data must be expanded into the matrix form for processing.
Disclosure of Invention
The invention aims to provide an electroencephalogram signal detection method based on a tensor method, which aims to solve the problems that the structure of original data can be damaged, the internal correlation of the data can be damaged and the like in the background technology.
The invention provides an electroencephalogram signal detection method based on a tensor method, which comprises the following steps:
step1, establishing a PARAFAC model based on the acquired electroencephalogram signals;
step2, extracting the psychological parameter characteristics of the electroencephalogram signals by adopting an alternative least square method to obtain a psychological parameter matrix, an electroencephalogram tester channel characteristic matrix and an acquisition environment matrix;
step3, performing identifiability condition analysis on the feature of the psychological parameter through the uniqueness of the PARAFAC model;
and 4, performing fast Fourier transform on a psychological generation mechanism and a psychological abnormal factor parameter of the electroencephalogram signal psychological parameter matrix to obtain an amplitude-frequency characteristic curve of the psychological parameter for later psychological diagnosis and treatment.
Compared with the prior art, the invention has the beneficial effects that:
the method establishes a PARAFAC model containing a channel characteristic matrix, a psychological characteristic parameter matrix and an acquisition environment matrix for the electroencephalogram signals. The extraction of the psychological characteristic parameters of the electroencephalogram signals is realized by using the PARAFAC model uniqueness theorem. FFT conversion is carried out on the specific channel to obtain an amplitude-frequency characteristic curve graph of each channel, and the mutual influence among the parameters can be analyzed according to the amplitude-frequency characteristic curve graph of each channel. Compared with other inventions, the method has the following obvious advantages: (1) Tensors have research space in the expression and analysis of high-dimensional data, and the internal structure of some data cannot be damaged; (2) The psychological characteristic parameters of the electroencephalogram signals are accurately detected and extracted.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of SNR-NMSE of a channel characterization parameter of the present invention;
FIG. 3 is a graph of the amplitude-frequency characteristic of the psychogenic mechanism of the present invention;
FIG. 4 is a graph showing the magnitude-frequency characteristics of the psychotropic factors of the present invention;
FIG. 5 is a graph of magnitude-frequency characteristics of the psychotropic factors of the present invention.
Detailed Description
The present invention is described in detail with reference to the embodiments shown in the drawings, but it should be understood that these embodiments are not intended to limit the present invention, and that functional, methodological, or structural equivalents thereof, which are equivalent or substituted by those of ordinary skill in the art, are within the scope of the present invention.
The embodiment provides an electroencephalogram signal detection method based on a tensor method, which comprises the following steps:
step1, establishing a PARAFAC model based on the acquired electroencephalogram signals;
step2, performing psychological parameter feature extraction on the electroencephalogram signal by adopting an alternating least square method (ALS) to obtain a psychological parameter matrix, an electroencephalogram tester channel characteristic matrix and an acquisition environment matrix;
step3, performing identifiability condition analysis on the feature of the psychological parameter through the uniqueness of the PARAFAC model;
and 4, performing fast Fourier transform on a psychological generation mechanism and psychological abnormal factor parameters of the electroencephalogram signal psychological parameter matrix to obtain an amplitude-frequency characteristic curve of the psychological parameters for later psychological diagnosis and treatment.
The invention has obvious advantages compared with other inventions, including:
(1) The tensor has a research space in the expression and analysis of high-dimensional data, the internal structure of some data cannot be damaged, and the tensor can model the data on the premise of not damaging the internal structure of some data, so that the tensor has a certain research space in the expression and analysis of a multi-dimensional state;
(2) The method can accurately detect and extract the psychological characteristic parameters of the electroencephalogram signals, is used as a multi-modal analysis tool, and tensor decomposition is also started to be used for electroencephalogram signal analysis, so that the method becomes a new research direction after time domain, frequency domain, time frequency and space-time analysis.
To verify the performance of the proposed algorithm, the method was analyzed using MATLAB simulation program. It should be noted that: once an item is defined in a drawing, it need not be further defined and explained in subsequent drawings.
Referring to fig. 1, fig. 1 is a flow chart of the present invention. The example is particularly applicable to a multi-dimensional state study space.
Step1, assuming that the channel characteristic of the electroencephalogram tester is represented by a, the psychological parameter of the tested human electroencephalogram signal is represented by b, and the electroencephalogram signal acquisition environment is represented by c, the acquired electroencephalogram signal can be written as follows:
Figure BDA0002774707440000031
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002774707440000032
noise and interference in the received electroencephalogram signals; i.e. i 1 、i 2 Respectively representing the number of channels at the receiving end of the sampling test and the corresponding ith 2 An individual subject; r is 1 、r 2 Respectively represent the r-th 1 The number of channels at the sending end of the test and the number of the psychological abnormal factors. The above equation can also be written as follows:
Figure BDA0002774707440000041
wherein i 2 ＝1,2,…,I 2 ，
Figure BDA00027747074400000416
Channel characteristic matrix of brain electrical tester respectively
Figure BDA0002774707440000042
Brain electrical signal psychological parameter matrix
Figure BDA0002774707440000043
Collection environment matrix
Figure BDA0002774707440000044
The elements (A) and (B) in (B),
Figure BDA0002774707440000045
for the purpose of matrix diagonalization operators,
Figure BDA00027747074400000417
for the ith in the received brain electric signal 2 Noise matrix of individual components.
Step2, the collected brain electrical signals are assumed to be
Figure BDA0002774707440000046
Firstly, a PARAFAC model is established for the collected electroencephalogram signal X, and the electroencephalogram signal for establishing the PARAFAC model is subjected to low-rank decomposition by utilizing an ALS algorithm. Wherein, the section operation is carried out on the EEG signal X measured by the EEG tester along the X direction to obtain the ith sub-section
Figure BDA0002774707440000047
Figure BDA00027747074400000418
Wherein, (.) T Denotes transposition, diag (. Circle.) as diagonalization operator, diag (A) i ) Represents a diagonal matrix formed by the ith row elements of the electroencephalogram signal parameter matrix A measured by the electroencephalogram tester. Arranging all the sub-section matrixes according to rows to obtain a section matrix along the x direction
Figure BDA0002774707440000048
Figure BDA0002774707440000049
Figure BDA00027747074400000410
Wherein [ ] indicates a Khatri-Rao product. Similarly, according to the formula (3), the electroencephalogram signal X measured by the electroencephalogram tester is respectively subjected to section interception along the y direction and the z direction to obtain a section matrix
Figure BDA00027747074400000411
And
Figure BDA00027747074400000412
X 2 ＝(B⊙C)A T (5)
X 3 ＝(C⊙A)B T (6)
and to the EEG signal X after the section 1 、X 2 、X 3 Performing ALS algorithm iterative estimation processing to obtain a channel characteristic matrix of the electroencephalogram tester
Figure BDA00027747074400000413
Matrix of brain electrical signals of tested person
Figure BDA00027747074400000414
And collecting the environment matrix
Figure BDA00027747074400000415
And finally, carrying out FFT (fast Fourier transform) on the psychology generation mechanism of the extracted electroencephalogram signal and the psychology abnormal factor psychology parameter channel to obtain an amplitude-frequency characteristic curve of the psychology parameters, and preparing for psychology diagnosis and treatment.
Step3, establishing a PARAFAC model for the electroencephalogram signals, wherein a channel characteristic matrix A of the electroencephalogram tester, a tested human electroencephalogram signal matrix B and an acquisition environment matrix C are respectively as follows:
C＝[(B⊙A) -1 ·X 3 ] T (7)
A＝[(C⊙B) -1 ·X 2 ] T (8)
B＝[(A⊙C) -1 ·X 1 ] T (9)
step4, identifiability condition analysis, and expressing k-rank of the matrix A as k A Even if any k of A A Column-linearly independent maximum integer k A . Similarly, k-rank of matrix B is denoted as k B K-rank of the matrix C is denoted as k C According to the PARAFAC model uniqueness theorem, the method can be obtained。
k A +k B +k C ≥2(R+1) (15)
Wherein R is the column dimension of the electroencephalogram signal. If the above formula is satisfied, the decomposition of A, B and C is unique.
The Step5 and ALS algorithms can respectively solve a channel characteristic matrix A, an electroencephalogram signal matrix B and an acquisition environment matrix C of the electroencephalogram tester. The method comprises the following implementation steps:
(1) Initializing a channel characteristic matrix A, an electroencephalogram signal matrix B and an acquisition environment matrix C of the electroencephalogram tester.
(2) Calculating the starting errors fit and fitold, wherein
Figure BDA0002774707440000051
fitold＝2*fit (11)
(3) According to a formula (3), an initialized electroencephalogram signal matrix B and a channel characteristic matrix A of the electroencephalogram tester are applied, and an acquisition environment matrix of the electroencephalogram signals is estimated to obtain:
Figure BDA0002774707440000052
(2) according to the formula (4), the estimated value of the acquisition matrix of the obtained brain electrical signals is utilized
Figure BDA0002774707440000053
And an initialized electroencephalogram signal matrix B, estimating a channel characteristic matrix of the electroencephalogram tester to obtain:
Figure BDA0002774707440000054
(3) according to the formula (5), the estimated value of the acquisition environment matrix of the acquired electroencephalogram signal is applied
Figure BDA0002774707440000055
Electroencephalogram and electroencephalogram testerIs estimated from the channel characteristic matrix
Figure BDA0002774707440000056
Estimating the electroencephalogram signal matrix B to obtain:
Figure BDA0002774707440000057
(4) The errors fit and fitold are recalculated.
(5) Repeating the steps (3) to (4) until the condition | (fit-fitold)/fitold | > smallndicar is satisfied, wherein smallndicar = eps.
(6) And carrying out matrix blurring and column blurring elimination operations on the obtained result.
(7) And extracting the electroencephalogram signal matrix B. The SNR-NMSE curve of the electroencephalogram tester channel characteristic parameter obtained by the ALS algorithm, as shown in fig. 2, can see that the normalized mean square error of the channel characteristic parameter decreases with the increase of the signal-to-noise ratio, which indicates that the extraction of the electroencephalogram tester channel characteristic matrix is correct.
(8) And performing FFT (fast Fourier transform) on the psychological generation mechanism and the psychological abnormal factor parameters of the tested human brain electrical signals to obtain an amplitude-frequency characteristic curve of the psychological parameters so as to facilitate the psychological diagnosis and treatment in the later period.
Psychological generation mechanism and psychological abnormal factor e of electroencephalogram signal of tested person 1 、e 2 The amplitude-frequency characteristic curves of (a) are shown in fig. 3 to 5. The psychological generation mechanism of the brain electrical signal is obviously changed between 0Hz and 20Hz, and the tested person has a depressed mood during the test. Accompanied by the change of psychological generation mechanism, a psychological abnormality factor e 1 And e 2 Corresponding changes have also occurred. Wherein the psychological abnormality factor e 1 Large variation range and psychological abnormal factor e 2 The variation amplitude is small. The change of the psychogenic mechanism in the frequency band is related to the psychogenic abnormality factor e 1 The influence is large, and besides large amplitude change between 0Hz and 40Hz, small amplitude fluctuation also occurs between 40Hz and 120 Hz. The tested person has low mood and lags behind during the test period and gradually tends to calm mindIn which small amplitude dips, calms and alternating changes in excited mood also occur. Therefore, the psychological generation mechanism and the parameter of the psychological abnormal factor fluctuate correspondingly. Because the measurable frequency range of the electroencephalogram signals is about 0-160 Hz, the amplitude of the amplitude-frequency characteristic curve chart is close to 0 after 160 Hz. Simulation results show that the channel characteristic parameters are normalized. The normalized mean square error is reduced along with the increase of the signal-to-noise ratio, and the correctness of the extraction of the electroencephalogram signal tester channel characteristic matrix is proved.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (1)

1. A brain electrical signal detection method based on a tensor method is characterized by comprising the following steps:
step1, assuming that the channel characteristic of the electroencephalogram tester is represented by a, the psychological parameter of the tested human electroencephalogram signal is represented by b, and the electroencephalogram signal acquisition environment is represented by c, the acquired electroencephalogram signal can be written as follows:
Figure FDA0003766667580000011
wherein the content of the first and second substances,
Figure FDA0003766667580000012
noise and interference in the received brain electrical signals; i.e. i 1 、i 2 Respectively representing the number of channels at the receiving end of the sampling test and the corresponding ith 2 An individual subject; r is 1 、r 2 Respectively represent the r-th 1 Psychological anomaly factor and test transmitting terminalThe number of channels; the above formula is written as follows:
Figure FDA0003766667580000013
wherein the content of the first and second substances,
Figure FDA0003766667580000014
channel characteristic matrix of brain electrical tester
Figure FDA0003766667580000015
Brain electrical signal psychological parameter matrix
Figure FDA0003766667580000016
Collection environment matrix
Figure FDA0003766667580000017
The elements in (A) and (B) are selected,
Figure FDA0003766667580000018
for the purpose of matrix diagonalization operators,
Figure FDA0003766667580000019
for the ith in the received brain electrical signal 2 A noise matrix of the individual components;
step2, the collected brain electrical signal is assumed to be
Figure FDA00037666675800000110
Firstly, establishing a PARAFAC model for an acquired electroencephalogram signal X, and performing low-rank decomposition on the electroencephalogram signal for establishing the PARAFAC model by utilizing an ALS algorithm; wherein, the section operation is carried out on the EEG signal X measured by the EEG tester along the X direction to obtain the ith sub-section
Figure FDA00037666675800000111
Figure FDA00037666675800000112
Wherein, (.) T Denotes the transposition, diag (. Cndot.) as diagonalization operator, diag (A) i ) Representing a diagonal matrix formed by the ith row elements of the electroencephalogram signal parameter matrix A measured by the electroencephalogram tester; arranging all the sub-section matrixes in rows to obtain a section matrix along the x direction
Figure FDA00037666675800000113
Figure FDA0003766667580000021
Wherein |, indicates a Khatri-Rao product; similarly, according to the formula (3), the electroencephalogram signal X measured by the electroencephalogram tester is respectively subjected to section interception along the y direction and the z direction to obtain a section matrix
Figure FDA0003766667580000022
And
Figure FDA0003766667580000023
X 2 ＝(B⊙C)A T (5)
X 3 ＝(C⊙A)B T (6)
and to the EEG signal X after the section 1 、X 2 、X 3 Performing ALS algorithm iterative estimation processing to obtain a channel characteristic matrix of the electroencephalogram tester
Figure FDA0003766667580000024
Matrix of brain electrical signals of tested person
Figure FDA0003766667580000025
And collecting the environment matrix
Figure FDA0003766667580000026
Finally, performing FFT (fast Fourier transform) on a psychology generation mechanism and a psychology abnormal factor psychology parameter channel of the extracted electroencephalogram signal to obtain an amplitude-frequency characteristic curve of the psychology parameters, and preparing for psychology diagnosis and treatment;
step3, establishing a PARAFAC model for the electroencephalogram signals, wherein a channel characteristic matrix A of the electroencephalogram tester, a tested human electroencephalogram signal matrix B and an acquisition environment matrix C are respectively as follows:
C＝[(B⊙A) -1 ·X 3 ] T (7)
A＝[(C⊙B) -1 ·X 2 ] T (8)
B＝[(A⊙C) -1 ·X 1 ] T (9)
step4, identifiability Condition analysis, representing k-rank of matrix A as k A Even if any k of A A Column-linearly independent maximum integer k A (ii) a Similarly, k-rank of matrix B is denoted as k B K-rank of the matrix C is denoted as k C According to the PARAFAC model uniqueness theorem, the method can be obtained
k A +k B +k C ≥2(R+1) (15)
Wherein R is the dimension of the electroencephalogram signal column, and the decomposition of A, B and C is unique when the above formula is satisfied;
step5, solving a channel characteristic matrix A, an electroencephalogram signal matrix B and an acquisition environment matrix C of the electroencephalogram tester by adopting an ALS algorithm; the method comprises the following implementation steps:
(1) Initializing a channel characteristic matrix A, an electroencephalogram signal matrix B and an acquisition environment matrix C of the electroencephalogram tester;
(2) Calculating the starting errors fit and fit, wherein
Figure FDA0003766667580000031
fitold＝2*fit (11)
(3) (1) according to a formula (3), applying an initialized electroencephalogram signal matrix B and a channel characteristic matrix A of the electroencephalogram tester to estimate an acquisition environment matrix of the electroencephalogram signals to obtain:
Figure FDA0003766667580000032
(2) according to the formula (4), the estimated value of the acquisition matrix of the obtained brain electrical signals is utilized
Figure FDA0003766667580000033
And an initialized electroencephalogram signal matrix B, estimating a channel characteristic matrix of the electroencephalogram tester to obtain:
Figure FDA0003766667580000034
(3) applying the estimated value of the acquisition environment matrix of the acquired electroencephalogram signal according to the formula (5)
Figure FDA0003766667580000035
And the estimated value of the channel characteristic matrix of the electroencephalogram tester
Figure FDA0003766667580000036
Estimating the electroencephalogram signal matrix B to obtain:
Figure FDA0003766667580000037
(4) Recalculating errors fit and fitold;
(5) Repeating the steps (3) to (4) until the condition | (fit-fitold)/fitold | > SMALLNUMBER is satisfied, wherein SMALLNUMBER = eps;
(6) Matrix fuzzy and column fuzzy elimination operations are carried out on the obtained result;
(7) Extracting an electroencephalogram signal matrix B; an SNR-NMSE curve graph of the electroencephalogram tester channel characteristic parameters is obtained through an ALS algorithm;
(8) And performing FFT (fast Fourier transform) on the psychological generation mechanism and the psychological abnormal factor parameters of the tested human brain electrical signals to obtain an amplitude-frequency characteristic curve of the psychological parameters so as to facilitate the psychological diagnosis and treatment in the later period.
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