Research On Signal Reconstruction Algorithm Based On Compressed Sensing

Compressed sensing theory is a new signal processing method.the theory has broken the limitation of Nyquist sampling theorem and use the lower rate to signal sampling and compression,set up a framework for recovering the original signal from a small number of sampling points,It effectively saves transmission,storage and other resources;Point the way to solve increasing demand for data processing.This paper mainly studies the signal reconstruction algorithm in compressed sensing theory,and discusses the improvement of signal reconstruction accuracy and reconstruction efficiency;Firstly this paper makes a brief described and analyzed to the theoretical framework and the three major contents of compressed sensing : sparse representation of signals,realization of measurement matrix and reconstruction algorithm,at the same time,four common measurement matrices are compared.Secondly,the classical signal reconstruction algorithm is introduced and matching tracking algorithm is focused on analysis.The OMP algorithm selects the atom with high accuracy,but cannot eliminate the error atom;The SP algorithm can eliminate the error atom of the support set by the idea of "backtracking".However,because of selecting multiple atoms to join the candidate support set,the accuracy is low;This paper presents a modified version of the OMP algorithm,The algorithm takes OMP algorithm as the main body,and uses SP algorithm to filter the atom again,which improves the precision of support set,Simulation results show that the reconstruction accuracy of this algorithm is greatly improved.Based on the fact that the number of sparsity is unknown in practical application,this paper presents an improved sparsity adaptive matching pursuit algorithm,The algorithm uses the step length method to replace the fixed step size of the conventional SAMP algorithm to improve the reconstruction efficiency of the signal and analyses the selection of the large step;In order to ensure the reconstruction accuracy of the signal,the improved algorithm mix up the cropping mechanism pruning the prediction support set,removing the wrong atom,Experimental results show that the reconstruction accuracy of this algorithm is slightly higher than that of SAMP algorithm,and the time for reconstruction is greatly reduced and the reconstruction efficiency is greatly improved,have better performance.Finally,this paper introduces a kind of "committee mechanism" fusion model,the fusion model can be used to fuse the two algorithms,and obtain a betterreconstruction effect than a signal reconstruction algorithm;In order to estimate the signal sparsity more accurately,use the Gini index to screen the atoms of the support set;In this paper,two sparsity adaptive matching pursuit algorithms are fused to verify the effectiveness of the fusion model,select the common atom of different algorithms' s support set as the right atom,next screening the remaining atoms by Gini index,thereby get the final support set.the experimental results show that the fusion algorithm has higher reconstruction accuracy and is suitable for any good signal reconstruction algorithm.