Research On Fast Signal Reconstruction Method Based On Sparse Representation

Sparse representation is widely used in various fields,such as image processing,machine learning,signal processing and many other fields,and has important roles such as noise reduction,deblurring,interpolation,etc.Due to the advantages and powerful adaptability of sparse representations,research applications of processing signals with sparse representation models are becoming more and more advanced,and the core of sparse representation models is the simple linear system equation,generated by the dictionary matrix H ∈Rn+m,using the signal described by y=Hx.According to different norm regularization criteria,the sparse representation models can be strictly classified into five forms:l0 norm minimization,lp norm(0<p<1)minimization,l1 norm minimization,l2 norm and l2,1 norm minimization of sparse representation models.Based on the sparse representation model,its main solution algorithms are divided into four major categories:greedy algorithm,approximation algorithm,homotopy algorithm and constrained optimization algorithm,while in the process of continuous research by scholars,there are more innovative combined solution methods,such as using Potts generalized function to build the model,and then using alternating direction multiplier method to solve;using threshold algorithm combined with conjugate gradient algorithm to solve the sparse representation model,etc.By sparse representation of the signal,the signal can be represented by fewer atoms in a given dictionary to achieve the purpose of concise representation of the signal,i.e,the use of sparse representation of the signal reconstruction to achieve the effect of noise reduction and denoising of the signal processing,so that it is easier and more accurate to obtain the real information contained in the signal,and facilitate further processing of the signal data.In the field of sensing and communication,the sparse representation model with fast weighted l1 norm number was used to solve the fiber Bragg grating signal;in the field of seismic detection,the dictionary training method was used to perform the sparse representation of seismic signal to achieve the separation of noise and effective signal,so as to make analysis of more accurate information,etc.It can be seen that sparse representation has been relatively mature in signal research.Reconstruction and denoising of signals can make subsequent research more real and effective,and surface electromyography signal is one of such actual research signals.Surface electromyography signal(SEMG)is a bioelectric signal that is generated due to muscle excitation and contraction,which can accurately reflect muscle activity and fatigue in real time,and is widely used in various fields.In clinical medicine,it is used for diagnosis of neuromuscular diseases;in rehabilitation medicine,it is used to detect the recovery status of patients’ limbs,etc.However,the surface electromyography signal is very weak as a biological signal,so there is inevitably noise generated by various factors that affect the signal during the acquisition process,applying the sparse representation to the surface electromyography signal can improve and reduce the impact of these noises,which is beneficial to the subsequent research.In this thesis,we first investigate the fast signal reconstruction method for sparse representation model,based on the l1 norm sparse representation model,the superposition optimization algorithm of this thesis is proposed in combination with the noise reduction framework,iterative soft thresholding algorithm and majorize-minimization algorithm,which can amplify the characteristics of the noise in the signal for better reconstruction and noise reduction.This thesis also analyzes the effect of the algorithm flow on the reconstruction of noisy signals in conjunction with experimental signals,and focuses on four sets of experimental simulations,the piecewise constant signal and the mixed signal are reconstructed for noise reduction under random noise,mixed noise composed of uniform and Gaussian conditions,respectively.Meanwhile,the majorize-minimization algorithm,iterative soft thresholding algorithm and the majorize-minimization superposition algorithm are also compared to verify the reconstruction noise reduction performance of this thesis,and compare the noise reduction error and noise reduction speed of the four algorithms,the experiments prove that the superposition optimization algorithm of this thesis can not only reconstruct the signal effectively in the face of different signals and different noises,but also perform better in terms of noise reduction error,and have a substantial improvement in noise reduction speed compared with the algorithm with the second smallest error,and the superposition optimization algorithm of this thesis has excellent comprehensive performance of reconstruction and noise reduction with effectiveness,accuracy and speed.This thesis not only verifies the effectiveness of the algorithm on the simulated signal,but also applies the superposition optimization algorithm to the actual surface electromyography signal to verify whether the reconstruction and noise reduction of the surface electromyography signal is effective,and whether it has a positive effect on the subsequent research of the surface electromyography signal.Experiments prove that the superposition optimization algorithm in this thesis can effectively apply to surface electromyography signal to reduce the effects of high-frequency noise and other effects,and improve the classification accuracy of surface electromyography signal and the accuracy of muscle fatigue prediction,experiments also prove the classification accuracy of the classification model proposed in this thesis for the acquired surface electromyography signal is high,and the support vector machine regression can make effective prediction of muscle fatigue.