A Research On The Algorithm For Accurate Reconstruction Of Piecewise Constant Signals Based On Total Variation Model

Signal reconstruction is one of the most widely studied subjects in the field of signal processing.Reconstruction is an essential step taken in signal processing in order to obtain effective signals in a faster and better manner.The main objective of signal reconstruction is to recover original signals from noise-containing signals as much as possible.The main sources of noise are disturbances from external environment during signal transmission and its own hardware systems.In certain vital application scenarios,such as determining the state of health by use of biological signals,and indicating the state of instruments and equipment by use of electrical signals,misdiagnose and industrial accidents may occur as a result of poor judgments because of signal pollution caused by noise.Therefore,it is of great significance to find an algorithm that can be used to accurately reconstruct signals.Total variation model has been widely studied and applied to the field of signal processing by virtue of its excellent smoothing effect and preservation of signal structure.Despite the excellent reconstruction performance of traditional total variation model in the smoothing processing of piecewise constant signals,the total variation model has a poor reconstruction performance at signal mutation due to the excessive smoothing of signals.In order to improve the reconstruction performance of the total variation model at signal mutation,the author,based on characteristics of regular terms and reconstructed signals of the total variation model,proposes a total variation model based on the mixing,superposition and optimization of difference matrix,which is capable of reconstructing piecewise constant signals with high quality in different noise environments.For regular terms,the author of this thesis redesigns regular terms and adjusts the weight of regular terms by enlarging and reducing the difference matrix without changing the regularization parameters so as to ensure a more reasonable proportion of regular terms at the mutation of piecewise constant signals and then improving the reconstruction performance and finally prove the universality of this algorithm under different noise conditions through experiments.For reconstructed signals,the author proposes to take the difference in reconstructed signals between the first and third time as a variation and integrate it with noise-containing signals to obtain a new noise-containing signal,send the new noise-containing signals to traditional total variation model for processing and finally prove this algorithm’s ability in processing different noise-containing signals through experiments.Afterwards,the improved total variation model is designed in combination of the advantages of the two algorithms,on the basis of mixing and superposition of difference matrix.The results show that combinatorial algorithm has a better processing performance in the case of mixed noise and that the optimization-minimization algorithm is selected as the algorithm to iteratively solve the model in this thesis.The simulation experiment also proves that under the condition of same experimental parameters,it is verified by comparing the SNR value,RMSE value and SSE value of different algorithms that the algorithm proposed in this thesis has higher accuracy in the reconstruction of piecewise constant signals.Finally,the author applies the algorithm proposed in this thesis to s EMG signal processing,and analyzes effectiveness of the algorithm in this thesis by comparing characteristic parameters of time domain and frequency domain as well as waveforms between post-reconstructed s EMG signals and original s EMG signals.The signals processed through the reconstruction method mentioned in this thesis is adopted to predict the fatigue state of the arm under different action states,analyze the influence of the algorithm proposed in this thesis on the prediction accuracy and make comparisons on the prediction accuracy of fatigue state through different combinations of characteristic parameters so as to figure out the combination of characteristic parameters most suitable for predicting the fatigue state under each action state.