Research Of Matching Pursuit Reconstruction Algorithms Based On Compressive Sensing

Compressed sensing theory improves the information collection rate by using the sparse characteristics of signals.As the key step of compressed sensing,reconstruction algorithms directly affect the quality of signal reconstruction.In this paper,the algorithms of matching pursuit in compressed sensing are studied.The specific innovations are as follows:(1)A stagewise iterative matching pursuit(StIMP)algorithm based on Moore-Penrose inverse is proposed.The StIMP algorithm first processes the Moore-Penrose generalized inverse for the observation matrix,and divides the iteration process into two stages.At the same time,the known sparsity is used to control the iterations.The simulation results show that,for 1D Gauss random signals,the proposed StIMP algorithm has the advantages of high success rate and strong robustness,the reconstruction error by the proposed StIMP algorithm is smaller as well;for 2D image signals,the proposed StIMP algorithm is more efficient and practical,because it could improve the reconstruction effect and greatly shorten the reconstruction time,and the image texture details by the proposed StIMP algorithm is more clear.(2)A double threshold iterative matching pursuit(DTSIMP)algorithm is proposed.The DTSIMP algorithm uses the idea of generalized inverse and two segment iterations of StIMP algorithm.However,unlike StIMP algorithm,the DTSIMP algorithm reduces the dependence on sparsity by threshold setting.The first threshold is set to control the first stage iteration to ensure the accurate input in the next stage,and the second threshold is set up to ensure the accuracy of the reconstruction.The simulation results show that the proposed DTSIMP algorithm has higher reconstruction success rate for 1D random Gauss signals,and has greater advantages in reconstruction quality and reconstruction time for 2D image signals.(3)A backtracking stagewise weak orthogonal matching pursuit algorithm based on fuzzy threshold(FTB-SWOMP)algorithm is proposed.The FTB-SWOMP algorithm,that can achieve reconstruction in the case of unknown sparsity,introduces backtracking strategy based on fuzzy threshold.The simulation results show that the proposed FTB-SWOMP algorithm can recover the 1D random Gauss signals at high probability.For 2D image signals,the proposed FTB-SWOMP algorithm has higher reconstruction quality,while time is equal to SWOMP algorithm.