Research Of Hard Thresholding Algorithms In Sparse Signal Recovery

Compressive sensing,is a new sampling method in recent years and have great value in many fields.Inspired by compressive sensing,the sparse recovery algorithms appear.We can class these algorithms into three categories: greedy methods,convex relaxation and hard thresholding algorithms.These three algorithms have their own advantages and limitations.The main contents and innovation can be summarized as follows:Firstly,we introduce some important concepts in compressive sensing.And We would analyze and introduce the three algorithms theoretically.Secondly,we propose the Projective Iterative Hard Thresholding Algorithm for sparse signal recovery in some particular conditions.And we theoretically prove its superiority with the numerical results.Thirdly,,we propose a new nonconvex model and we obtain a new greedy method by applying the nonconvex method PL-IRLS on this nonconvex model.Then we prove its property by the numerical results.At last,we analyze the two algorithms in practice,and compare the results.