Electrical signal decomposition method based on short-time variational mode decomposition and electroencephalogram signal decomposition device

Abstract

The application discloses a kind of based on short-time variational modal decomposition electric signal decomposition method, comprising: step 1, obtaining initial electric signal, using pre-constructed window function to the electric signal is carried out sliding window operation, obtain the signal segment corresponding to the electric signal;Step 2, set reconstruction mode number, using variational problem to describe the mode constraint condition of each mode under sliding window signal segment, obtain constraint optimization function;Step 3, using augmented Lagrange function to carry out equivalent transformation to constraint optimization function, solve and obtain unconstrained optimization function;Step 4, reconstruct to unconstrained optimization function, obtain the instantaneous frequency-time function corresponding to each mode electric signal.This application provides a kind of electroencephalogram signal decomposition device.The method provided by the application does not need to define base function in advance, is completely driven by original signal data decomposition, can eliminate mode aliasing and edge effect problem, to obtain the complete electric signal corresponding to each rhythm.

Description

Technical Field

[0001] This invention relates to the technical field of electrical signal decomposition and reconstruction, and in particular to an electrical signal decomposition method and an electroencephalogram (EEG) signal decomposition device based on short-time variational mode decomposition. Background Technology

[0002] Electroencephalogram (EEG) signals are the overall reflection of the electrophysiological activity of brain nerve tissue on the surface of the cerebral cortex. EEG signals can be acquired by placing electrode sensors outside the cerebral cortex. Currently, EEG signals are widely used in brain-computer interfaces (BCIs) due to their low cost and non-invasive nature. External devices acquire the user's EEG signals, process and analyze them to determine the type of imagery activity the user is currently performing, thereby controlling the device to complete the corresponding task.

[0003] Neurophysiological studies have shown that when a specific cortical region of the brain is active, the amplitude of a particular rhythm in the EEG signal decreases; this physiological phenomenon is called event-related desynchronization (ERD). Conversely, when the brain is in a resting or inactive state, the amplitude of a particular rhythm increases; this physiological phenomenon is called event-related synchronization (ERS). Therefore, ERD and ERS phenomena are important indicators for determining brain activity. Consequently, obtaining the types and temporal ranges of ERD and ERS is a crucial approach to analyzing brain imagery activity through EEG signals.

[0004] However, EEG signals themselves are non-stationary and have low signal-to-noise ratios, making direct analysis of the raw signal difficult. In practical applications, preprocessing and feature extraction of the raw signal are necessary before using other algorithms to analyze the processed signal. Most preprocessing methods employ existing time-frequency analysis techniques, such as wavelet transform and empirical mode decomposition (EMD). However, these methods each have their own limitations. For example, wavelet transform requires predefined basis functions and cannot provide a highly concentrated time-frequency representation of the EEG signal; EMD suffers from limitations such as mode aliasing and edge effects, and cannot effectively separate signal components of different rhythms.

[0005] Patent document CN114145757A discloses a method for reconstructing electroencephalogram (EEG) signals based on an asymmetric synthesis filter bank. This method includes: acquiring raw EEG signals; preprocessing the raw EEG signals to obtain their spectrum; setting the division boundaries of the raw EEG signals based on the spectrum; introducing an analysis filter bank with downsamplers; setting the total number of channels in the analysis filter bank; and setting the filter coefficients and the sampling rate of each channel's downsampler according to the division boundaries; inputting the raw EEG signals into the analysis filter bank for filtering and downsampling to obtain the analysis filter bank matrix after filtering and downsampling; determining the frequency response of the filter corresponding to each channel in the asymmetric synthesis filter bank based on the synthesis matrix; and inputting several downsampled EEG signals from the analysis filter bank into the asymmetric synthesis filter bank for reconstruction to obtain the reconstructed EEG signals. This method requires the pre-construction of an asymmetric synthesis filter bank, which demands high anti-interference capabilities from the filter bank.

[0006] Patent document CN113935380A discloses a method and system for an adaptive motor imagery brain-computer interface based on template matching, comprising the following steps: first, preprocessing and feature extraction and optimization of EEG signals based on motor imagery; then, designing a template matching classification model based on adaptive rules. After acquiring EEG signals, this invention first preprocesses the EEG signals, then extracts and optimizes their features. Next, using training data and external auxiliary information, and fusing adaptive rules, template information for different motor imagery signals is obtained. This allows for the establishment of an EEG signal classification model based on template matching to identify motor imagery intentions. By establishing a motor imagery EEG signal recognition model based on adaptive rules using template matching, the motor imagery brain-computer interface can stably recognize motor imagery intentions during long-term use. This method requires pre-setting basis functions and training the model; however, using the model to preprocess the data may result in data loss. Summary of the Invention

[0007] To address the aforementioned issues, this invention provides an electrical signal decomposition method based on short-time variational mode decomposition. This method does not require pre-defined basis functions and can completely obtain the EEG signal components of different rhythms in the EEG signal, which helps to detect ERD and ERS phenomena, thereby improving the accuracy of brain-computer interface devices in analyzing human brain motor imagery tasks.

[0008] An electrical signal decomposition method based on short-time variational mode decomposition includes:

[0009] Step 1: Obtain the initial electrical signal, and use a pre-constructed window function to perform a sliding window operation on the electrical signal to obtain the signal segment corresponding to the electrical signal;

[0010] Step 2: Set the number of reconstructed modes, use variational problems to describe the modal constraints of each mode's sliding window signal segment, and obtain the corresponding constraint optimization function;

[0011] Step 3: Use the augmented Lagrangian function to perform an equivalent transformation on the constrained optimization function obtained in Step 2 to obtain the corresponding unconstrained optimization function;

[0012] Step 4: Reconstruct the unconstrained optimization function obtained in Step 3 to obtain the instantaneous frequency-time function corresponding to each modal electrical signal.

[0013] This invention organically combines the concept of variational mode decomposition with the framework of short-time Fourier transform. Without the need to predefine basis functions, it can directly process raw EEG signals to obtain the instantaneous frequency-time function corresponding to the pure EEG signal.

[0014] Specifically, the electrical signal in step 1 is an electroencephalogram (EEG) signal, which is acquired through a brain-computer interface device. The EEG signal is an important indicator for predicting human brain activity.

[0015] Preferably, the specific process of step 1 is as follows:

[0016] Step 1-1: Model the electrical signal to obtain the corresponding amplitude modulation and frequency modulation signals;

[0017] Step 1-2: Perform sliding window operation on the amplitude-modulated and frequency-modulated signals obtained in step 1-1 in the time domain using a window function.

[0018] Preferably, the specific process of step 2 is as follows:

[0019] Step 2-1: Set the number of reconstructed modes based on the input electrical signal;

[0020] Step 2-2: Extend the electrical signal through mirroring operation;

[0021] Steps 2-3: Perform Hilbert transform on the expanded electrical signal to obtain the corresponding analytic signal;

[0022] Step 2-4: Substitute the analytic signal obtained in Step 2-3 into the adjustment operator and mix it with the spectrum. With the goal of minimizing the bandwidth of the analytic signal, construct the corresponding constrained optimization function. The specific expression of the constrained optimization function is as follows:

[0023]

[0024] Where, {u1,u2,···u K} represents all modes under a given window, {ω1,ω2,...,ω... K} represents all center frequencies within a given window. is the conjugate function of the window function. This represents the signal frame obtained by multiplying the k-th mode with the window function at time t0, where the window function is centered at the window function. δ is the impulse function. This represents a system parameter that, when convolved with a signal frame, yields the analyzed signal representation of that frame. This indicates the first derivative with respect to time.

[0025] Preferably, the unconstrained optimization function in step 3 is obtained by solving the equivalent transformed constrained optimization function using the alternating multiplier method.

[0026] Preferably, the expression for the unconstrained optimization function in step 3 is as follows:

[0027]

[0028] Where STFT represents the time spectrum obtained by performing a short-time Fourier transform on the electrical signal, f represents the initial electrical signal, τ represents the time of the time spectrum, ω represents the frequency of the time spectrum, the superscript n represents the result obtained after the nth iteration, λ is the Lagrange multiplier, and α is the penalty term parameter.

[0029] Preferably, the expression for the reconstructed unconstrained optimization function is as follows:

[0030]

[0031] in, The center frequency of the k-th mode at time σ is represented by the superscript n, which indicates the result obtained after the nth iteration. τ represents the time of the time spectrum, and ω represents the frequency of the time spectrum.

[0032] The present invention also provides an electroencephalogram (EEG) signal decomposition device, including a computer memory, a computer processor, and a computer program stored in the computer memory and executable on the computer processor. The computer memory executes the above-described electroencephalogram decomposition method based on short-time variational mode decomposition. When the computer processor executes the computer program, it performs the following steps: inputting an initial EEG signal, analyzing and calculating it according to the EEG signal decomposition method, and outputting time-frequency diagrams corresponding to each decomposed EEG modality.

[0033] Compared with the prior art, the beneficial effects of the present invention include:

[0034] (1) No basis functions need to be predefined. The decomposition is driven entirely by the original signal data, which can obtain a highly concentrated time-frequency representation.

[0035] (2) There is no modal aliasing or edge effect, and the signals corresponding to each rhythm can be completely decomposed to obtain a pure EEG signal time-frequency map. Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating the electrical signal decomposition method based on short-time variational mode decomposition provided by the present invention.

[0037] Figure 2 This is a schematic diagram of the rhythm amplitude obtained by EEG signal decomposition provided in this embodiment;

[0038] Figure 3 This is a schematic diagram of the rhythm power obtained by EEG signal decomposition in this embodiment;

[0039] Figure 4 The time-frequency diagrams of each channel signal obtained after EEG signal decomposition in this embodiment are shown. Detailed Implementation

[0040] Because human brain signals are very complex, even small external noises can contaminate them, causing brain-computer interfaces (BCIs) that use brain signals to obtain instructions to recognize the correct information. Therefore, this embodiment proposes an effective method for removing noise from electrical signals and for processing electrical signals that is applicable to BCI devices.

[0041] like Figure 1 As shown, an electrical signal decomposition method based on short-time variational mode decomposition includes:

[0042] Step 1: Obtain the initial EEG signal, and use a pre-constructed window function to perform a sliding window operation on the EEG signal to obtain the signal segment corresponding to the EEG signal.

[0043] Among them, electroencephalogram (EEG) signals are acquired through brain-computer interface devices and are an important indicator for predicting human brain activity.

[0044] Step 1-1: Model the EEG signal to obtain the corresponding amplitude-modulated and frequency-modulated signals;

[0045] Step 1-2: Perform sliding window operation on the amplitude-modulated and frequency-modulated signals obtained in step 1-1 in the time domain using a window function.

[0046] Step 2: Set the number of reconstructed modes, use variational problems to describe the modal constraints of each mode's sliding window signal segment, and obtain the corresponding constraint optimization function;

[0047] Step 2-1: Set the number of reconstructed modalities based on the input EEG signals;

[0048] Step 2-2: Expand the EEG signal through mirroring;

[0049] Steps 2-3: Perform Hilbert transform on the expanded EEG signal to obtain the corresponding analytical signal;

[0050] Step 2-4: Substitute the analytic signal obtained in Step 2-3 into the adjustment operator and mix it with the spectrum. With the goal of minimizing the bandwidth of the analytic signal, construct the corresponding constrained optimization function. The specific expression of the constrained optimization function is as follows:

[0051]

[0052] Where, {u1,u2,···u K} represents all modes under a given window, {ω1,ω2,...,ω... K} represents all center frequencies within a given window. is the conjugate function of the window function. This represents the signal frame obtained by multiplying the k-th mode with the window function at time t0, where the window function is centered at the window function. δ is the impulse function. This represents a system parameter that, when convolved with a signal frame, yields the analyzed signal representation of that frame. This indicates the first derivative with respect to time.

[0053] Step 3: To solve the above optimization problem, the augmented Lagrangian function is first constructed as follows:

[0054]

[0055] Where, {u1,u2,···u K} represents all modes under a given window, {ω1,ω2,...,ω... K} represents all center frequencies within a given window, τ represents the time of the time spectrum, λ is the Lagrange multiplier, and α is the penalty term parameter. is the conjugate function of the window function. This represents the signal frame obtained by multiplying the k-th mode with the window function at time t0, where the window function is centered at the window function. δ is the impulse function. This represents a system parameter, which, when convolved with an electrical signal frame, yields an analyzed signal representation of the signal frame. This represents the first derivative with respect to time;

[0056] For each sliding window corresponding to the time scale τ, the optimization problem is as follows:

[0057]

[0058]

[0059]

[0060] Using the alternating direction multiplier method The solution is as follows:

[0061]

[0062] The superscript n denotes the result obtained in the nth iteration. Due to the equivalence of the Fourier transform, the optimization problem is transformed into a Fourier domain solution using Parseval's theorem as follows:

[0063]

[0064] By setting the gradient of the constructed Lagrange equation to zero, the TFR expression for each mode can be obtained:

[0065]

[0066] Where STFT represents the time spectrum obtained by performing a short-time Fourier transform on the electrical signal, f represents the initial electrical signal, τ represents the time of the time spectrum, ω represents the frequency of the time spectrum, the superscript n represents the result obtained after the nth iteration, λ is the Lagrange multiplier, and α is the penalty term parameter. Due to the narrowband characteristics of each mode under the short time window, the corresponding TFR reduces the influence of spectral leakage, the Heisenberg uncertainty principle, and noise interference, thus displaying more concentrated time-frequency information.

[0067] Step 4: Reconstruct the unconstrained optimization function obtained in Step 3 using ISTFT:

[0068]

[0069] Where, {u1,u2,···u K} represents all modes under a given window, τ represents the time of the time spectrum, ω represents the frequency of the time spectrum, and λ is the Lagrange multiplier;

[0070] Finally, the instantaneous frequency-time function corresponding to each modal electrical signal is obtained:

[0071]

[0072] in, The center frequency of the k-th mode at time τ is represented, the superscript n indicates the result obtained after the nth iteration, τ represents the time of the time spectrum, and ω represents the frequency of the time spectrum.

[0073] Under an appropriate window, the instantaneous frequency information can be characterized by its center frequency. Therefore, by sequentially combining and connecting the center frequencies of each mode under each window, the instantaneous frequency of each mode can be obtained.

[0074] This embodiment also provides an electroencephalogram (EEG) signal decomposition device, including a computer memory, a computer processor, and a computer program stored in the computer memory and executable on the computer processor, wherein the above-described electroencephalogram (EEG) signal decomposition method based on short-time variational mode decomposition is executed in the computer memory.

[0075] When the computer processor executes the computer program, it performs the following steps: inputting an initial EEG signal, analyzing and calculating it according to the electrical signal decomposition method, and outputting the time-frequency diagrams corresponding to each modality of EEG signal after decomposition.

[0076] This device can be used as the host computer module of a finger rehabilitation training system, which includes a computer acquisition device, a computer for processing data, a finger rehabilitation training mechanical mechanism, and a matching controller.

[0077] When a user uses this device, they imagine movements in their mind. The EEG signal decomposition device receives the EEG signals obtained from the brain electrical signal acquisition and processes the electrical signals according to the decomposition method provided by this invention. The decomposition obtains the time-frequency diagrams corresponding to each modality of EEG signal. By judging the user's current motor imagination task, the device generates corresponding control signals and sends them to the controller. The controller drives the finger rehabilitation training mechanical mechanism to move the user's fingers to perform rehabilitation training, thereby completing the function of real-time feedback training.

[0078] To illustrate the effectiveness of this invention, a set of real EEG signals is used as an example to explain the implementation scheme and effects of this multi-component signal decomposition method based on variational mode decomposition. The EEG signals used in the implementation come from the publicly available BCI Competition IV Dataset I dataset. During the signal acquisition process, the subject was performing a left-hand motor imagery task (the subject is usually a patient who cannot move their limbs independently after surgery and needs rehabilitation training).

[0079] In this embodiment, the brain-computer interface device selected is a postoperative limb rehabilitation training machine, which allows patients to complete rehabilitation training activities independently, thereby reducing the workload of caregivers.

[0080] In the experiment, signals from two channels, C3 and C4, were acquired and decomposed using the method of this invention.

[0081] like Figure 2The diagram shows the amplitude of the rhythms obtained from signal decomposition. The left diagram shows the amplitude of the Beta rhythm, and the right diagram shows the amplitude of the Mu rhythm. Note that the first 2 seconds and the last 2 seconds in the diagram correspond to the fixed crosshair and blank screen display phases during signal acquisition, respectively. During the middle 4 seconds, the subjects performed a motor imagery task. The signal diagram shows that ERD occurs between 1.5 and 4 seconds in the C4 channel signal, and ERS occurs around 3 seconds in the C3 channel.

[0082] like Figure 3 The diagram shows the rhythm power obtained from signal decomposition. The left diagram shows the power of the Beta rhythm, and the right diagram shows the power of the Mu rhythm. The power diagrams also reveal the timing and corresponding channels of ERD and ERS occurrences.

[0083] like Figure 4 As shown, the time-frequency diagrams of each channel signal obtained after signal decomposition are presented, with the left diagram representing channel C3 and the right diagram representing channel C4. These time-frequency diagrams are obtained by calculating the Hilbert-Huang transform of the signal. It can also be seen from the time-frequency diagrams that the energy of the C4 channel signal decreases between 1.5 and 4 seconds, corresponding to the ERD phenomenon; the energy of the C3 channel signal increases around 3 seconds, corresponding to the ERS phenomenon. The above experimental results demonstrate that the electrical signal decomposition method based on short-time variational mode decomposition proposed in this invention can effectively enhance the features in the signal, helping to better identify the timing and corresponding channels of ERD and ERS phenomena in the signal.

Claims

1. A method for decomposing electrical signals based on short-time variational mode decomposition, characterized in that, include: Step 1: Obtain the initial electrical signal, and perform sliding window operation on the electrical signal using a pre-constructed window function to obtain the signal segment corresponding to the electrical signal. The electrical signal in Step 1 is an electroencephalogram (EEG) signal, which is acquired through a brain-computer interface device. The specific process of step 1 is as follows: Step 1-1: Model the electrical signal to obtain the corresponding amplitude modulation and frequency modulation signals; Step 1-2: Perform sliding window operation on the amplitude-modulated and frequency-modulated signals obtained in step 1-1 in the time domain using a window function. Step 2: Set the number of reconstructed modes, use variational problems to describe the modal constraints of each mode's sliding window signal segment, and obtain the corresponding constraint optimization function; The specific process of step 2 is as follows: Step 2-1: Set the number of reconstructed modes based on the input electrical signal; Step 2-2: Extend the electrical signal through mirroring operation; Steps 2-3: Perform Hilbert transform on the expanded electrical signal to obtain the corresponding analytic signal; Step 2-4: Substitute the analytic signal obtained in Step 2-3 into the adjustment operator and mix it with the spectrum. With the goal of minimizing the bandwidth of the analytic signal, construct the corresponding constrained optimization function. The specific expression of the constrained optimization function is as follows: Where, {u1,u2,···u K } represents all modes under a given window, {ω1,ω2,...,ω... K } represents all center frequencies within a given window. is the conjugate function of the window function. This represents the signal frame obtained by multiplying the k-th mode with the window function at time t0, where the window function is centered at the window function. δ is the impulse function. This represents a system parameter. This represents the first derivative with respect to time; Step 3: Apply the augmented Lagrangian function to the constrained optimization function obtained in Step 2 to perform an equivalent transformation, and solve for the corresponding unconstrained optimization function. The expression of the unconstrained optimization function in Step 3 is as follows: Where STFT represents the time spectrum obtained by performing a short-time Fourier transform on the electrical signal, f represents the initial electrical signal obtained, τ represents the time of the time spectrum, ω represents the frequency of the time spectrum, the superscript n represents the result obtained after the nth iteration, λ is the Lagrange multiplier, and α is the penalty term parameter; Step 4: Reconstruct the unconstrained optimization function obtained in Step 3 to obtain the instantaneous frequency-time function corresponding to each modal electrical signal. The expression of the reconstructed unconstrained optimization function is as follows: in, ω represents the center frequency of the k-th mode at time τ, the superscript n indicates the result obtained after the nth iteration, τ represents the time of the time spectrum, and ω represents the frequency of the time spectrum.

2. The electrical signal decomposition method based on short-time variational mode decomposition according to claim 1, characterized in that, The unconstrained optimization function in step 3 is obtained by solving the equivalent transformed constrained optimization function using the alternating multiplier method.

3. A brainwave signal decomposition device, comprising a computer memory, a computer processor, and a computer program stored in the computer memory and executable on the computer processor, characterized in that, The computer memory executes the electrical signal decomposition method based on short-time variational mode decomposition as described in any one of claims 1-2; When the computer processor executes the computer program, it performs the following steps: inputting an initial EEG signal, analyzing and calculating it according to the EEG signal decomposition method, and outputting the time-frequency diagrams corresponding to each modality of the decomposed EEG signal.

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