Researchs Of Linearized Bregman Iteration And Its Application In Compressed Sensing

Bregman iteration is one of the effective methods which were rised in recent years to solvesparse problem, and it has an important value in a lot of applications such as image processing andCompressed Sensing.This paper focuses on the study of linearized Bregman iteration and its application toCompressed Sensing, main innovation work are as follows:(1) proposed FL-Bregman iteration based on―residue back‖. FL-Bregman iteration is a newmethod based on linearized Bregman iteration and―residue back‖. It updated observed value inevery iteration to rise the convergent rate. Then this paper applied FL-Bregman iteration toCompressed Sensing, the experiment result indicated that FL-Bregman iteration would gain afaster convergent rate than linearized Bregman iteration and also be robust to noise.(2) proposed a generalized inverse matrix A--FL-Bregman iteration based on delinquent fullrank matrix. A--FL-Bregman is a method which used the generalized inverse of observed matix tosolve delinquent full rank observed matrix problem. This paper gave the convergence of newmethods and then applied them to Compressed Sensing, the experiment result indicated thatA--FL-Bregman iteration algorithm can reconstruct the original signal when observed matrix isdelinquent full and also gain a faster convergent rate than A--Bregman iteration algorithm.(3) proposed block sparse FL-Bregman iteration and block sparse A--FL-Bregman iteration.Block sparse FL-Bregman iteration focus on a particular sparse model-block sparse model. Andthen this paper applied block sparse FL-Bregman iteration to Compressed Sensing, the experimentresult indicated that block sparse algorithm can get a better reconstruction quality then generalmethod.