A Modified Iterative Shrinkage-Thresholding Algorithm

The fast iterative shrinkage-thresholding algorithm (FISTA) is proposed by Amir Beck and Marc Teboulle [SIAM Imaging Science,2009,2(1):183-202] based on iterative shrinkage-thresholding algorithm. When solving the linear inverse problems in singal and image processing, the FISTA has a faster speed than ISTA. In this paper, we introduce the idea of line search methods and proposed a modified iterative shrinkage-thresholding algorithm. We obtain the global convergence of the new algorithm when the blur operator (A) is given. The experimental results show that, compared with the ISTA and FISTA the new algorithm not only gets the clearer pictures, but also has the smaller error value in the analysis of the data.