Reweighted fast iterative shrinkage thresholding algorithm with restarts for l 1 ‐ l 1 minimisation

Abstract

For solving the l 1-l 1 minimisation problem, the authors propose a reweighted fast iterative shrinkage thresholding algorithm. The proposed algorithm consists of two steps: in the first step, the authors apply the smoothing technique to l 1-l 1 minimisation; and in the second step the smoothed problem is solved by fast iterative shrinkage thresholding algorithm (FISTA). With the help of restarts technique, the authors further accelerate the reweighted FISTA algorithm. Compared with some provable and efficient existing methods, the methods proposed in this study enjoy faster speed, less parameters and that the convergent analysis does not need any assumption of A. On the computational level, numerical experiments on sparse signal recovery demonstrate the efficiency of the proposed methods.