CN115299960A - Electric signal decomposition method and electroencephalogram signal decomposition device based on short-time varying separate modal decomposition - Google Patents
Electric signal decomposition method and electroencephalogram signal decomposition device based on short-time varying separate modal decomposition Download PDFInfo
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Abstract
The invention discloses an electric signal decomposition method based on short-time varying mode decomposition, which comprises the following steps: step 1, acquiring an initial electric signal, and performing sliding window operation on the electric signal by using a pre-constructed window function to obtain a signal section corresponding to the electric signal; step 2, setting a reconstruction modal number, describing modal constraint conditions of the gliding window signal segments of each modal by adopting a variational problem, and obtaining a constraint optimization function; step 3, carrying out equivalent transformation on the constrained optimization function by adopting an augmented Lagrange function, and solving to obtain an unconstrained optimization function; and 4, reconstructing the unconstrained optimization function to obtain an instantaneous frequency-time function corresponding to each modal electric signal. The invention provides an electroencephalogram signal decomposition device. The method provided by the invention does not need to define a basis function in advance, is completely driven and decomposed by original signal data, and can eliminate the problems of mode aliasing and edge effect, thereby obtaining a complete electric signal corresponding to each rhythm.
Description
Technical Field
The invention relates to the technical field of electric signal decomposition and reconstruction, in particular to an electric signal decomposition method and an electroencephalogram signal decomposition device based on short-time division modal decomposition.
Background
Electroencephalography (EEG) is a general reflection of the electrophysiological activity of cranial nerve tissue on the surface of the cerebral cortex. The electrode sensor is placed outside the cerebral cortex, and the electroencephalogram signals can be acquired. Currently, because of its low cost and non-invasive characteristics, EEG signals are widely used in Brain Computer Interface (BCI). The external equipment collects the electroencephalogram signals of the user, and the imagination activity type executed by the current user can be judged through processing and analyzing, so that the equipment is controlled to complete corresponding tasks.
Neurophysiological studies have shown that the amplitude of specific rhythms in EEG signals will decrease when certain cortical regions of the brain are active, a physiological phenomenon known as event-related desynchronization (ERD); when the brain is at rest or in an indolent state, the amplitude of a particular rhythm will rise, a physiological phenomenon known as event-related synchronization (ERS). It can be seen that the ERD and ERS phenomena are important criteria for determining brain activity. Therefore, the acquisition of the category and the appearance time range of ERD and ERS is an important way to analyze brain imagination activity through EEG signals.
However, EEG signals are inherently characterized by non-stationary, low signal-to-noise ratios, and there are difficulties in analyzing directly from the raw signals. In practical application, the original signal needs to be preprocessed and feature extracted, and then the processed signal needs to be analyzed by other algorithms. Most of the preprocessing methods use the existing time-frequency analysis technology, such as wavelet transform, empirical Mode Decomposition (EMD), etc. However, the above methods have their own limitations in applications, such as wavelet transform that requires pre-defined basis functions and does not provide a time-frequency representation of highly focused EEG signals; EMD has limitations such as modal aliasing and edge effects, and cannot perfectly separate signal components of different rhythms.
Patent document CN114145757A discloses an electroencephalogram signal reconstruction method based on an asymmetric synthesis filter bank, which includes: acquiring an original brain electrical signal, and preprocessing the original brain electrical signal to obtain a frequency spectrum of the original brain electrical signal; setting a partition boundary of an original electroencephalogram signal based on a frequency spectrum, introducing an analysis filter bank of a lower sampler, setting the total number of channels of the analysis filter bank, and setting the coefficient of the filter and the sampling rate of a lower sampler of each channel according to the partition boundary; inputting the original brain electrical signal into an analysis filter bank for filtering and downsampling to obtain a matrix of the filter bank which is subjected to filtering and downsampling sampling rate calculation analysis; determining the frequency response of a filter corresponding to each channel in the asymmetric synthesis filter bank according to the synthesis matrix; and respectively inputting a plurality of brain wave signals subjected to down-sampling by the analysis filter bank into the asymmetric synthesis filter bank for reconstruction to obtain reconstructed brain wave signals. The method needs to construct an asymmetric synthesis filter bank in advance, and has higher requirement on the anti-interference capability of the filter bank.
Patent document CN113935380A discloses a template matching-based adaptive motor imagery brain-computer interface method and system, including the following steps: firstly, preprocessing electroencephalogram signals based on motor imagery, extracting and optimizing features, and then designing a template matching classification model based on a self-adaptive rule; according to the invention, after an electroencephalogram signal is collected, the electroencephalogram signal is preprocessed, then the characteristics of the electroencephalogram signal are extracted and optimized, next, training data and external auxiliary information are utilized, and self-adaption rules are fused to obtain template information of different motor imagery signals, further, an electroencephalogram signal classification model based on template matching is established, a motor imagery intention is identified, and a motor imagery electroencephalogram signal identification model is established through the self-adaption rules based on template matching, so that the motor imagery brain-computer interface can stably identify the motor imagery intention in long-term use. The method needs to set a basis function in advance, train a model of the basis function, and preprocess data by adopting the model, so that the problem of data loss may occur.
Disclosure of Invention
In order to solve the problems, the invention provides an electric signal decomposition method based on short-time varying separate mode decomposition, which can completely obtain EEG signal components with different rhythms in EEG signals without defining basis functions in advance, is beneficial to detecting ERD and ERS phenomena, and thus improves the analysis accuracy of brain-computer interface equipment on human brain motor imagination tasks.
An electric signal decomposition method based on short-time division modal decomposition comprises the following steps:
and 4, reconstructing the unconstrained optimization function obtained in the step 3 to obtain an instantaneous frequency-time function corresponding to each modal electric signal.
The invention organically combines the concept of variation modal decomposition with the framework of short-time Fourier transform, does not need to define a basis function in advance, and can directly carry out data processing on the original electroencephalogram signal, thereby obtaining the instantaneous frequency-time function corresponding to the pure electroencephalogram signal.
Specifically, the electrical signal in step 1 is an electroencephalogram signal, and is acquired through a brain-computer interface device, and the electroencephalogram signal is an important index for predicting human brain activity.
Preferably, the specific process of step 1 is as follows:
step 1-1, modeling the electric signal to obtain a corresponding amplitude modulation and frequency modulation signal;
and step 1-2, performing sliding window operation on the amplitude modulation and frequency modulation signal obtained in the step 1-1 in a time domain through a window function.
Preferably, the specific process of step 2 is as follows:
step 2-1, setting a reconstruction modal number according to the input electric signal;
2-2, expanding the electric signal through mirror image operation;
step 2-3, carrying out Hilbert transformation on the expanded electric signals to obtain corresponding analytic signals;
step 2-4, bringing the analytic signals obtained in the step 2-3 into a regulating operator to be mixed with the frequency spectrum, and constructing and obtaining a corresponding constraint optimization function by taking the bandwidth minimization of the analytic signals as a target, wherein the specific expression of the constraint optimization function is as follows:
wherein, { u 1 ,u 2 ,···u K Denotes all modes under a given window, { ω 1 ,ω 2 ,···,ω K Denotes all center frequencies under a given window,
is a conjugate function of the window function and,
representing the centre of the window function at t 0 The k-th mode at the moment is multiplied by the window function to obtain a signal frame, delta is an impulse function,
representing a system parameter which is convolved with the signal frame to obtain an analysis signal representation of the signal frame,
indicating the first derivative with respect to time.
Preferably, the unconstrained optimization function in step 3 is obtained by solving the constrained optimization function after the equivalent transformation by using an alternating multiplier method.
Preferably, the expression of the unconstrained optimization function in step 3 is as follows:
the STFT represents a time-frequency spectrum obtained by short-time Fourier transform of an electric signal, f represents an obtained initial electric signal, tau represents time of the time-frequency spectrum, omega represents frequency of the time-frequency spectrum, superscript n represents a result obtained after nth iteration operation, lambda is a Lagrange multiplier, and alpha is a penalty term parameter.
Preferably, the result expression reconstructed by the unconstrained optimization function is as follows:
wherein,
the central frequency of the kth mode at the time sigma is shown, the superscript n shows the result obtained after the nth iteration operation, the time of the time spectrum is shown by tau, and the frequency of the time spectrum is shown by omega.
The invention also provides an electroencephalogram signal decomposition device, which comprises a computer memory, a computer processor and a computer program stored in the computer memory and executable on the computer processor, wherein the computer memory executes the electrical signal decomposition method based on short-time division modal decomposition; the computer processor, when executing the computer program, performs the steps of: inputting an initial electroencephalogram signal, carrying out analysis and calculation according to an electroencephalogram signal decomposition method, and outputting a time-frequency graph corresponding to each mode of electroencephalogram signal after decomposition.
Compared with the prior art, the invention has the beneficial effects that:
(1) The decomposition is completely driven by original signal data without pre-defining basis functions, and highly centralized time-frequency representation can be obtained.
(2) The method has no modal aliasing and edge effect, and can completely decompose and obtain signals corresponding to each rhythm, thereby obtaining a pure electroencephalogram time-frequency image.
Drawings
FIG. 1 is a schematic flow chart of an electrical signal decomposition method based on short-time differential modal decomposition according to the present invention;
FIG. 2 is a schematic diagram of the rhythm amplitude obtained by the decomposition of the EEG signal provided in the present embodiment;
FIG. 3 is a schematic diagram of the rhythm power obtained by decomposing the EEG signal provided in this embodiment;
fig. 4 is a time-frequency diagram of each channel signal obtained after the EEG signal provided by this embodiment is decomposed.
Detailed Description
Because the human brain electrical signal is very complex, some external fine noise can pollute the electrical signal, and the brain-computer interface for acquiring the brain electrical signal instruction cannot identify correct information, the embodiment provides an electrical signal processing method which can effectively remove the electrical signal noise and is suitable for brain-computer interface equipment.
As shown in fig. 1, an electrical signal decomposition method based on short-time division modal decomposition includes:
The brain electrical signals are acquired through a brain-computer interface device, and the brain electrical signals are important indexes for predicting brain activities of human bodies.
Step 1-1, modeling the electroencephalogram signal to obtain a corresponding amplitude modulation and frequency modulation signal;
and step 1-2, performing sliding window operation on the amplitude modulation and frequency modulation signal obtained in the step 1-1 in a time domain through a window function.
2-1, setting a reconstruction modal number according to an input electroencephalogram signal;
step 2-2, expanding the electroencephalogram signal through mirror image operation;
2-3, performing Hilbert transformation on the expanded electroencephalogram signal to obtain a corresponding analytic signal;
step 2-4, bringing the analytic signals obtained in the step 2-3 into a regulating operator to be mixed with the frequency spectrum, and constructing and obtaining a corresponding constraint optimization function by taking the bandwidth minimization of the analytic signals as a target, wherein the specific expression of the constraint optimization function is as follows:
wherein, { u { 1 ,u 2 ,···u K Denotes all modes under a given window, { ω 1 ,ω 2 ,···,ω K Denotes all center frequencies under a given window,
is a conjugate function of the window function and,
representing the center of the window function at t 0 The k-th mode at the moment is multiplied by the window function to obtain a signal frame, delta is an impulse function,
representing a system parameter which is convolved with the signal frame to obtain an analysis signal representation of the signal frame,
indicating the first derivative with respect to time.
wherein, { u 1 ,u 2 ,···u K Denotes all modes under a given window, { ω 1 ,ω 2 ,···,ω K Denotes all center frequencies under a given window, τ denotes time of the time spectrum, λ is the lagrange multiplier, α is the penalty parameter,
is a conjugate function of the window function and,
representing the centre of the window function at t 0 The k-th mode at the moment is multiplied by the window function to obtain a signal frame, delta is an impulse function,
representing a system parameter which is convolved with the frame of electrical signal to obtain an analysis signal representation of the frame of signal,
representing the first derivative with respect to time;
for the time scale τ corresponding to each sliding window, the optimization problem is as follows:
using pairs of multipliers of alternating directions
Solving is carried out, and the concrete formula is as follows:
where the superscript n denotes the result of the nth iteration. Due to the equivalence of fourier transform, the optimization problem is transformed into the fourier domain using the Parseval theorem and solved as follows:
setting the gradient of the constructed lagrangian equation to zero, the TFR expression of each mode can be obtained:
the STFT represents a time-frequency spectrum obtained by performing short-time Fourier transform on an electric signal, f represents an obtained initial electric signal, tau represents time of the time-frequency spectrum, omega represents frequency of the time-frequency spectrum, superscript n represents a result obtained after nth iteration operation, lambda is a Lagrange multiplier, and alpha is a penalty term parameter; due to the narrow-band characteristic of each mode in a short time window, the corresponding TFR reduces the influence of spectrum leakage, heisenberg uncertainty principle and noise interference, thereby displaying more concentrated time-frequency information.
wherein, { u 1 ,u 2 ,···u K Represents all modes under a given window, τ represents time of the time spectrum, ω represents frequency of the time spectrum, and λ is a lagrange multiplier;
finally, the instantaneous frequency-time function corresponding to each modal electric signal is obtained:
wherein,
representing the central frequency of the kth mode at the time tau, wherein the superscript n represents the result obtained after the nth iteration operation, tau represents the time of the time spectrum, and omega represents the frequency of the time spectrum;
the frequency information of the instantaneous frequency can be characterized by the center frequency of the instantaneous frequency under a proper window, so that the instantaneous frequency of each mode is obtained by respectively combining and connecting the center frequencies of each mode under each window in sequence.
The embodiment also provides an electroencephalogram signal decomposition apparatus, which comprises a computer memory, a computer processor and a computer program stored in the computer memory and executable on the computer processor, wherein the computer memory executes the above-mentioned electrical signal decomposition method based on short-time division modal decomposition;
the computer program when executed by a computer processor implements the steps of: inputting an initial electroencephalogram signal, carrying out analysis and calculation according to an electric signal decomposition method, and outputting a time-frequency graph corresponding to each mode electroencephalogram signal after decomposition.
The device can be used as an upper computer module of a finger rehabilitation training system, and the finger rehabilitation training system comprises a computer acquisition device, a computer for processing data, a finger rehabilitation training mechanical mechanism and a controller used in a matched mode.
When a user uses the equipment, the user can imagine actions in the brain, the electroencephalogram signal decomposition device receives electroencephalogram signals acquired by brain electrical signals, the electrical signals are processed according to the decomposition method provided by the invention, time-frequency graphs corresponding to the electroencephalogram signals in various modes are obtained by decomposition, corresponding control signals are generated and sent to the controller by judging the motor imagery task of the user at the moment, and the controller drives the finger rehabilitation training mechanical mechanism to drive the fingers of the user to perform rehabilitation training, so that the function of real-time feedback training is completed.
For the purpose of illustrating the implementation effect of the present invention, the implementation and effect of the multi-component signal decomposition method based on variational modal decomposition are described by taking a set of real EEG signals as an example. The EEG signals used in the implementation were from a public data set BCI composition IV Dataset I, the subject being performing a left hand motor imagery task during the signal acquisition (subject is usually a patient with no voluntary post-operative limb activity, requiring rehabilitation training).
The brain-computer interface device selected for the embodiment is a postoperative limb rehabilitation training machine, and can enable a patient to independently complete rehabilitation training activities, so that the working pressure of a worker is relieved.
Signals of two channels of C3 and C4 are collected in the experiment and are decomposed by the method of the invention.
As shown in FIG. 2, the amplitude diagram of the rhythm obtained by signal decomposition is shown, wherein the left diagram is the amplitude diagram of the Beta rhythm, and the right diagram is the amplitude diagram of the Mu rhythm. Note that the first 2 seconds and the second 2 seconds of the figure correspond to the fixed cross and blank screen display links in the signal acquisition process, respectively, and the motor imagery task is tried to be executed within 4 seconds in the middle. As can be seen from the signal diagram, ERD occurs within 1.5 seconds to 4 seconds of the C4 channel signal, and ERS occurs around 3 seconds of the C3 channel.
As shown in FIG. 3, the power diagram of the rhythm obtained by signal decomposition is shown, wherein the left diagram is the power diagram of Beta rhythm, and the right diagram is the power diagram of Mu rhythm. Through the power diagram, the time when ERD and ERS appear and the corresponding channel can be observed as well.
As shown in fig. 4, a time-frequency diagram of each channel signal obtained after signal decomposition is shown, where the left diagram is a C3 channel and the right diagram is a C4 channel. The time-frequency diagram is obtained by calculating Hilbert-Huang transform of the signal, and the energy of the C4 channel signal is weakened within 1.5 seconds to 4 seconds and corresponds to an ERD phenomenon as can be seen from the time-frequency diagram of the signal; the energy of the C3 channel signal rises around 3 seconds, corresponding to the ERS phenomenon. The above experimental results prove that the electric signal decomposition method based on the short-time division modal decomposition provided by the invention can effectively enhance the characteristics in the signal and is beneficial to better identifying the occurrence time and the corresponding channel of the ERD and ERS phenomena in the signal.
Claims (8)
1. An electric signal decomposition method based on short-time division modal decomposition is characterized by comprising the following steps:
step 1, acquiring an initial electric signal, and performing sliding window operation on the electric signal by using a pre-constructed window function to obtain a signal section corresponding to the electric signal;
step 2, setting a reconstruction modal number, describing modal constraint conditions of the gliding window signal segments of each modal by adopting a variational problem, and obtaining a corresponding constraint optimization function;
step 3, carrying out equivalent transformation on the constrained optimization function obtained in the step 2 by adopting an augmented Lagrange function, and solving to obtain a corresponding unconstrained optimization function;
and 4, reconstructing the unconstrained optimization function obtained in the step 3 to obtain an instantaneous frequency-time function corresponding to each modal electric signal.
2. The electrical signal decomposition method based on short-time varying fractional modal decomposition according to claim 1, wherein the electrical signal in step 1 is an electroencephalogram signal, which is acquired through a brain-computer interface device and is an important index for predicting brain activities of a human body.
3. The electrical signal decomposition method based on short-time division modal decomposition according to claim 1, wherein the specific process of step 1 is as follows:
step 1-1, modeling the electric signal to obtain a corresponding amplitude modulation and frequency modulation signal;
and step 1-2, performing sliding window operation on the amplitude modulation and frequency modulation signal obtained in the step 1-1 in a time domain through a window function.
4. The electrical signal decomposition method based on short-time division modal decomposition according to claim 1, wherein the specific process of the step 2 is as follows:
step 2-1, setting a reconstruction modal number according to the input electric signal;
step 2-2, expanding the electric signal through mirror image operation;
step 2-3, carrying out Hilbert transformation on the expanded electric signals to obtain corresponding analytic signals;
step 2-4, bringing the analytic signals obtained in the step 2-3 into a regulating operator to be mixed with the frequency spectrum, and constructing and obtaining a corresponding constraint optimization function by taking the bandwidth minimization of the analytic signals as a target, wherein the specific expression of the constraint optimization function is as follows:
wherein, { u 1 ,u 2 ,…u K Denotes all modes under a given window, { ω 1 ,ω 2 ,…,ω K Denotes all center frequencies under a given window,
is a conjugate function of the window function and,
representing the centre of the window function at t 0 The k-th mode at the moment is multiplied by the window function to obtain a signal frame, delta is an impulse function,
it is shown that a parameter of the system,
indicating the first derivative with respect to time.
5. The electrical signal decomposition method based on short-time varying fractional modal decomposition according to claim 1, wherein the unconstrained optimization function in the step 3 is obtained by solving the constrained optimization function after the equivalent transformation by using an alternating multiplier method.
6. The electrical signal decomposition method based on short-time differential modal decomposition according to claim 1, wherein the unconstrained optimization function in the step 3 is expressed as follows:
the STFT represents a time-frequency spectrum obtained by short-time Fourier transform of an electric signal, f represents an obtained initial electric signal, tau represents time of the time-frequency spectrum, omega represents frequency of the time-frequency spectrum, superscript n represents a result obtained after nth iteration operation, lambda is a Lagrange multiplier, and alpha is a penalty term parameter.
7. The electrical signal decomposition method based on short-time differential modal decomposition according to claim 1, wherein the result expression reconstructed by the unconstrained optimization function is as follows:
wherein,
the central frequency of the kth mode at the time tau is shown, the superscript n shows the result obtained after the nth iteration operation, tau shows the time of the time spectrum, and omega shows the frequency of the time spectrum.
8. An electroencephalographic signal decomposition apparatus comprising a computer memory, a computer processor, and a computer program stored in and executable on said computer memory, wherein said computer memory executes therein the electrical signal decomposition method based on short-time-variant modal decomposition according to any one of claims 1 to 7; the computer processor, when executing the computer program, performs the steps of: inputting an initial electroencephalogram signal, carrying out analysis and calculation according to an electroencephalogram signal decomposition method, and outputting a time-frequency graph corresponding to each mode electroencephalogram signal after decomposition.
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| CN115500829A (en) * | 2022-11-24 | 2022-12-23 | 广东美赛尔细胞生物科技有限公司 | Depression detection and analysis system applied to neurology |
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