阅读说明：本技术 基于小波变换和全变差正则化的信号去噪方法 (Signal denoising method based on wavelet transformation and total variation regularization ) 是由 杨利军 丁思佳 周锋 杨晓慧 刘风瑞 于 2020-06-16 设计创作，主要内容包括：本发明公开了一种基于小波变换和全变差正则化的信号去噪方法。包括：对含有噪声的脑电信号y(n)进行小波阈值去噪；计算信号y(n)与小波阈值去噪后信号<Image he="58" wi="89" file="DDA0002542335040000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>的余量；对余量d(n)利用全变差正则化进行去噪；将去噪后的信号重构,得到干净信号的估计值；根据去噪评价指标评估脑电信号去噪性能。利用本发明,可以在信号去噪场景中,一方面放松小波阈值去噪中的阈值选择对去噪效果的影响；另一方面保护信号边缘信息,使得去噪后的信号不出现局部震荡,以得到更好的去噪效果。(The invention discloses a signal denoising method based on wavelet transformation and total variation regularization. The method comprises the following steps: carrying out wavelet threshold denoising on the electroencephalogram signal y (n) containing noise; calculating signal y (n) and de-noised signal of wavelet threshold The balance of (2); denoising the residual d (n) by total variation regularization; reconstructing the denoised signal to obtain an estimated value of a clean signal; and evaluating the denoising performance of the electroencephalogram signal according to the denoising evaluation index. By using the method, the influence of threshold selection in wavelet threshold denoising on the denoising effect can be relaxed on the one hand in a signal denoising scene; and on the other hand, the signal edge information is protected, so that the denoised signal does not have local oscillation, and a better denoising effect is obtained.)

1. A signal denoising method based on wavelet transform and total variation regularization is characterized by comprising the following steps:

step 1, performing wavelet threshold denoising on a signal y (n) containing noise:

step 1a, performing wavelet decomposition on a signal y (n) to obtain each scale coefficient;

step 1b, setting a threshold value for each scale coefficient obtained after wavelet decomposition, and further obtaining an exact estimation value of a clean signal wavelet coefficient through threshold value processing;

step 1c, performing inverse wavelet transform according to the exact wavelet coefficient estimation value of the clean signal, thereby realizing reconstruction of the signal and obtaining the signal after denoising of the wavelet threshold

Step 2, calculating signals y (n) and signals after wavelet threshold denoising

step 3, denoising the residual d (n) by using total variation regularization:

step 3a, establishing a total variation regularization denoising model for the margin:

where D is the residual signal, D is the first order difference matrix,

and 3b, converting the denoising model in the step 3a into an unconstrained optimization model:

wherein λ ═ λ (λ)₁；λ₂；…λ_N-1) For augmenting Lagrange multipliers, p is a penalty parameter,

Translating an unconstrained optimization model into a model for

Step 4, reconstructing the denoised signal in the step 1 and the denoised signal in the step 3 to obtain an estimated value of the clean signal:

wherein x (n) is an estimated value of the clean signal;

and 5, evaluating the signal denoising performance according to the denoising evaluation index.

2. The method of claim 1, wherein the translating an unconstrained optimization model into a model for the optimizationu, lambda optimization model, using ADMM algorithm pairCarrying out iterative operation on the u and lambda optimization models to obtain a denoising margin signal

converting an unconstrained optimization model to a model foru and lambda optimization model:

to pair

3. The method of claim 1, wherein the denoising evaluation indicator in step 5 comprises:

root mean square error RMSE:

wherein N represents the signal length, s (N) is the signal before noise addition, and x (N) is the signal after noise removal;

signal-to-noise ratio SNR:

wherein N represents the total length of the signal, s (N) is the signal before noise addition, and x (N) is the signal after noise removal;

pearson correlation coefficient ρ:

wherein N represents the total length of the signal, s (N) is the signal before noise addition, x (N) is the signal after noise removal,is the average value of the signal before the addition of noise,

Technical Field

The invention relates to the technical field of signal denoising, in particular to a signal denoising method based on wavelet transformation and total variation regularization.

Background

The electrical activity of the brain is caused by spontaneous, rhythmic potential changes produced by neurons of the cerebral cortex, and the sum of the electrical activity of local neurons recorded from the extracranial scalp or intracranially is called an electroencephalogram. In recent years, the rapid development of electronic computing science and the development of artificial intelligence inject new force for the progress of diagnosis and treatment by applying electroencephalogram signals, so far, the electroencephalogram signals become important medical indexes for evaluating brain functions and are applied to the research and diagnosis of a plurality of central nervous system diseases. Electroencephalograms can be classified into cerebral cortex electroencephalograms, deep electroencephalograms, scalp electroencephalograms, and the like according to differences in the positions of electrodes placed on the head. The electroencephalogram acquisition mode has good stability, the obtained electroencephalogram signal has high signal-to-noise ratio, but the electroencephalogram acquisition mode needs to be implanted into the brain, so that the electroencephalogram acquisition mode has certain trauma to a patient, and the scalp electroencephalogram is widely applied to practical clinical detection. The electrode position of the scalp electroencephalogram is on the surface of the scalp, and the method is a non-invasive acquisition mode, but the electroencephalogram signals acquired by the acquisition mode are weak, are easily influenced by noise in the acquisition process, and can have great influence on classification results. How to process and obtain clean and effective electroencephalogram signals is the key for carrying out subsequent analysis on the electroencephalogram signals, so that denoising processing on the electroencephalogram signals before analysis is an important research content.

According to the acquisition process of the electroencephalogram signals, the interference sources of the noises are mainly divided into two categories: one is noise of the detection system itself, such as noise of contact between the scalp and the electrodes, interference of alternating current power supply and electromagnetic, and the like; the other type is noise generated by physiological electric signals such as blinking, muscle movement, heartbeat and the like when the electroencephalogram signals are acquired. The removal of EEG signal noise is an important research content in the EEG signal processing process, the commonly adopted method is to remove noise through Fourier transform, but EEG signal is a nonlinear non-stationary signal, Fourier transform is a signal processing method provided for stationary signals, so certain defects exist, along with the development of wavelet theory, wavelet transform is widely applied in EEG signal denoising, in 1994, Carmona, R.A and Hudgins, L.H applies wavelet transform to the denoising field at the earliest; later Herrera, R.E and the like utilize a wavelet transformation soft threshold denoising method to denoise electroencephalogram signals; zhou Weidong et al combine wavelet transform with independent component analysis to separate the electrocardio-interference and myo-electric interference in the electroencephalogram signals; the electroencephalogram signal denoising is firstly researched in China by Wu Xiaopei et al in 2000, and the electroencephalogram signal is researched by the electroencephalogram pulse interference elimination technology based on orthogonal wavelet transformation, and because the electroencephalogram signal contains a large amount of transient information of different frequency components, the wavelet transformation is more effective in electroencephalogram signal processing compared with the traditional Fourier analysis method; then, Wuping et al propose an electroencephalogram signal analysis method based on an autoregressive model (ARM) and wavelet transformation, and utilize the method to eliminate noise interference in the electroencephalogram signal; in 2012, juveno et al have proposed an electroencephalogram signal denoising method based on improved EMD, in order to eliminate the end point effect of EMD, the end point of the electroencephalogram signal needs to be extended, and the extended EMD method is used to denoise EEG, so that the noise in the signal can be effectively removed, but the process is more complicated compared with wavelet transformation.

The wavelet transform is a multi-resolution time-scale analysis method, which can divide signals into sub-band signals of different frequency bands, and can more effectively and flexibly detect and remove noise interference in electroencephalogram signals by utilizing the wavelet transform, so that the research for denoising electroencephalogram signals in China and abroad is mainly based on the wavelet transform for processing, but the wavelet transform has some defects in the processing: local oscillation easily occurs on the signal after wavelet transformation denoising; when wavelet threshold denoising is adopted, the selection of the threshold function and the threshold has great influence on the denoising result, and the over-large or over-small threshold can influence the denoising effect and further influence the classification result.

Disclosure of Invention

The invention provides a signal denoising method based on wavelet transformation and total variation regularization, which realizes signal denoising and simultaneously relaxes the influence of threshold selection in wavelet threshold denoising on the denoising effect; and on the other hand, the signal edge information is protected, so that the denoised signal does not have local oscillation, and a better denoising effect is obtained.

A signal denoising method based on wavelet transform and total variation regularization comprises the following steps:

step 1, performing wavelet threshold denoising on a signal y (n) containing noise:

step 1a, performing wavelet decomposition on a signal y (n) to obtain each scale coefficient;

step 1b, setting a threshold value for each scale coefficient obtained after wavelet decomposition, and further obtaining an exact estimation value of a clean signal wavelet coefficient through threshold value processing;

step 1c, performing inverse wavelet transform according to the exact wavelet coefficient estimation value of the clean signal, thereby realizing reconstruction of the signal and obtaining the signal after denoising of the wavelet threshold

Step 2, calculating signals y (n) and signals after wavelet threshold denoisingThe balance of (2):

step 3, denoising the residual d (n) by using total variation regularization:

step 3a, establishing a total variation regularization denoising model for the margin:

where D is the residual signal, D is the first order difference matrix,

denoising the residual signal, and performing total variation denoising on the residual signal again to reserve a useful signal as much as possible and remove a noise signal; the first part is fidelity item, which ensures the transportationIn the calculation process, the difference between the two signals before and after denoising is not too large, the second part is a total variation regularization term, and the parameter α is used for adjusting the weight;

and 3b, converting the denoising model in the step 3a into an unconstrained optimization model:

wherein λ ═ λ (λ)₁；λ₂；…λ_N-1) For augmenting Lagrange multipliers, p is a penalty parameter,constraint of u obedience

Translating an unconstrained optimization model into a model foru, lambda optimization model, using ADMM algorithm pairCarrying out iterative operation on the u and lambda optimization models to obtain a denoising margin signal

Step 4, reconstructing the denoised signal in the step 1 and the denoised signal in the step 3 to obtain an estimated value of the clean signal:

wherein x (n) is an estimated value of the clean signal;

and 5, evaluating the signal denoising performance according to the denoising evaluation index.

Translating an unconstrained optimization model into a model for

u, lambda optimization model, using ADMM algorithm pair

Carrying out iterative operation on the u and lambda optimization models to obtain a denoising margin signalThe method comprises the following steps:

converting an unconstrained optimization model to a model foru and lambda optimization model:

to pairThe optimization model of u and lambda is subjected to iterative operation untilStopping iteration when the error bound is larger than or equal to the error bound or the iteration times is larger than the maximum iteration times to obtain a de-noising residual signal

The denoising evaluation index in the step 5 comprises:

root mean square error RMSE:

wherein N represents the signal length, s (N) is the signal before noise addition, and x (N) is the signal after noise removal;

signal-to-noise ratio SNR:

wherein N represents the total length of the signal, s (N) is the signal before noise addition, and x (N) is the signal after noise removal;

pearson correlation coefficient ρ:

wherein N represents the total length of the signal, s (N) is the signal before noise addition, x (N) is the signal after noise removal,is the average value of the signal before the addition of noise,is the average value of the denoised signal.

The invention has the beneficial effects that:

the invention provides a new denoising method by combining a wavelet transform denoising algorithm and total variation regularization, on one hand, the influence of threshold selection in wavelet threshold denoising on the denoising effect is relaxed, the denoised signal is processed, useful information is kept as much as possible, and the noise signal is removed; on the other hand, signal edge information is protected by means of total variation denoising, so that the denoised signal does not have local oscillation, and a better denoising effect is obtained.

Drawings

FIG. 1 is a flow chart of signal denoising based on wavelet transform and total variation regularization;

FIG. 2 is a flow chart of wavelet transform threshold denoising;

FIG. 3 is a comparison graph of denoising effects of bump test signals;

fig. 4 is a graphical illustration of the SNR values of the humps test signal at different noise levels.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The invention provides a signal denoising method based on wavelet transformation and total variation regularization. Designing a two-step denoising strategy based on wavelet transformation and total variation regularization, then solving a total variation regularization model by using an alternative direction multiplier (ADMM) algorithm, and finally measuring the denoising effect of the model in an algorithm experiment and a real electroencephalogram signal denoising experiment by using some common evaluation indexes. The signal denoising process based on total variation regularization and wavelet transform is shown in fig. 1. The following description will be made by way of specific examples.