Research And Application On Matching Pursuit Reconstruction Algorithms For Compressed Sensing

With the development of information society,the amount of information to be processed is increasing rapidly and the application scenarios become more and more complicated.Compressed Sensing theory provides a way to sample and compress sparse signals at a low sampling rate;by directly projecting the original high-dimensional signal to the low dimension,and then recovering the original signal accurately by the reconstruction algorithm,which greatly relieves the pressure of sampling and storage.Reconstruction algorithm is the key of Compressed Sensing theory in practical application,and how to improve the performance of reconstruction algorithm(reconstruction accuracy,reconstruction speed,anti-interference ability,etc.)has been a hot spot in the research area.Focusing on the greedy algorithms in compressed sensing,this paper proposes three improved algorithms after analyzing the limitations of the existing reconstruction performance in different scenarios.Finally,the validation are verified through computer simulation.The main contents are as follows:Firstly,to address the problem that the Generalized Orthogonal Matching Pursuit(GOMP)algorithm is not able to correct the wrong atoms,the SGOMP(Subspace Generalized Orthogonal Matching Pursuit)algorithm is proposed.By leveraging the idea of subspace pursuit and choosing appropriate node of subspace pursuit,the proposed method is able to correct the wrong atoms,and therefore,the possibility is increased for the final atoms support to converge to the correct subspace.Consequently,the reconstruction accuracy and reconstruction speed are improved at the same time.Moreover,the algorithm can also recover signal in low signal to noise ratio scenario,showing good anti-noise performance.Secondly,taking advantage of the traversal of tree structure,the Fast Multipath Matching Pursuit(FMMP)algorithm based on the pruning strategy is put forward.The reduced unnecessary search path,and restriction in the number of candidates along with the improved atom selection strategy overcome the problem of high computational complexity caused by the tree breadth-first search,and avoid the lack of support set optimization resulting from the tree depth-first search.Thus,the reconstruction time is reduced while the accuracy of the reconstruction is ensured.Finally,a Variable Step Length Sparsity Adaptive Matching Pursuit(VSLSAMP)algorithm is proposed.A strategy of variable step length based on the arctangent function is applied to solve the problem of SAMP algorithm that the accuracy and reconstruction speed cannot be guaranteed at the same time by using fixed step length approach in the phase of sparsity estimation.Besides that a threshold selection strategy is introduced at the stage of signal recovering,and the algorithm reconstruction precision is improved by reducing the possibility of selecting error atoms.As a result,the VSLSAMP algorithm has a higher SNR in both noiseless and different noise environments,and the reconstruction time is reduced by more than 50%.