Two Kinds Of Algorithms Based On Matching Pursuit Algorithms In Sparse Signal Recovery

With the development of information age,it is difficult for traditional sampling methods to meet people’s increasing needs of information sampling and storage.The appearance of compressed sensing breaks through the bottleneck of traditional sampling methods.It can sample and compress sparse signals through a small amount of information,realize the signal projection from high dimension to low dimension,and then restore the original signal by the reconstruction algorithm,which reduces the demand for signal transmission and storage.Reconstruction algorithm is the key to apply compressed sensing from theory to practice.How to improve the performance of reconstruction algorithm is always a hot research topic.Based on this,this thesis studies classical matching pursuit algorithms in compressed sensing,analyzes the limitations of current algorithms,proposes a new algorithm in view of existing problems,and verifies the performance of the improved algorithm through numerical experiments.The main contents of this thesis are as follows:1.Atoms selected by Orthogonal Matching Pursuit(OMP)algorithm is not orthogonal optimal globally,resulting in a low probability of successful signal reconstruction.In this thesis,Iterative Reweighted Least Squares(IRLS)algorithm is used to weight the sparse matrix of OMP algorithm.Iterative Reweighted Orthogonal Matching Pursuit(IROMP)algorithm is proposed.In this algorithm,the non-optimal atoms are changed to 0 by weighted method,which increasing the probability of correct selection of atoms.Experimental results show that the probability of successful reconstruction of IROMP algorithm is higher compared with other matching pursuit algorithms.2.Due to the Generalized Orthogonal Matching Pursuit(GOMP)algorithm,atoms are selected by the inner product method,resulting in poor reconstruction performance.In this thesis,Jaccard matching criterion is improved and introduced into GOMP algorithm.A Improved Jaccard Generalized Orthogonal Matching Pursuit(IJGOMP)algorithm is proposed.The performance of the algorithm is verified by numerical experiments,and the improved algorithm is applied to remote sensing image restoration.Compared with OMP algorithm and JGOMP algorithm,the proposed algorithm has better effect on image detail restoration.