SAR Image Restoration Based On Bregman Iteration Method

Sparse representation is using simple sparse structure to represent the information of interest.Because it needs only fewer signal,it attracts wide attention.However,finding the optimal sparse expansion is known to be NP hard question and in general there are two methods to solve the problem.The first one is to look for the equivalent function of the original question,then use the hard threshold operator to solve directly.Under the condition of equivalent changing the original question into the convex optimization question is the second method.Due to Bregman iteration has many advantages in signal and image recovery question which are the sparse optimization question,we propose a new algorithm to solve SAR images sparse optimal filtering question based on the₁l norm optimization theory and Bregman iterative regularization theory.In this paper we also study M-sparse iterative hard threshold algorithm and propose a new modified M-sparse iterative thresholding algorithm,termed as MIHT.The innovation of this paper mainly reflect in the following two aspects.Firstly,we propose a new algorithm for SAR images sparse optimal filtering question by combining the SAR image filtering optimal model and the split Bregman iterative thought.The numerical experiments is carried from the equivalent number of looks and edge preservation index aspects between our algorithm and other commonly used methods.Fortunately,our algorithm has a good recovery effect.Secondly,with the use of the equivalent form of the least square problem and the original M-sparse algorithm presented by T.Blumensath and M.E.Davies,a modified M-sparse iterative thresholding algorithm?termed as MIHT?for sparse approximation problem is deduced and the theoretical convergence is given by fundamental calculus tools.The numerical experiments for solving large numbers of small to medium over-determined and under-determined problems show that the improved algorithm can improve the results calculated by IHT method and other methods such as OMP,ROMP,BIHT and CoSaMP.