Projection Algorithm For The Problem Of 1 Problem In Compression Sensing

A computationally-efficient method for recovering sparse signals is known as the problem of compressed sensing(CS). In the paper, we solved 0l-norm problem via their convex relaxations. More precisely, we replace the 0l-norm by 1l-norm. The convex relaxations problem of compressed sensing is transformed into a convex feasibility problem(CFP) which is solved by using projection methods, convex relaxation method and successive projection relaxation method. At last, the algorithms and results are illustrated by several numerical examples. The paper is divided into four chapters.The first chapter introduced the application backgrounds, the research situations and conversion process of the 0l-norm problem of compressed sensing.In second chapter, we first transform the convex relaxed problem of compressed sensing into a convex feasibility problem. Then, a projection method is presented to solve it. In addition, we get the global convergence.In third chapter, we consider to relax projection method because it is difficult to project to the set. Therefore, convex relaxation method is applied for these problems. In addition, global convergence is proved. In last, the algorithms and results are illustrated by several numerical examples.In fourth chapter, the first problem is solved by successive projection relaxation method. And global convergence is proved. In the last, the algorithms and results are illustrated by several numerical examples.