Accelerated proximal algorithms for L1-minimization problem

Linearized Bregman algorithm is effective on solving l1-minimization problem, but its parameter's selection must rely on prior information. In order to ameliorate this weakness, we proposed a new algorithm in this paper, which combines the proximal point algorithm and the linearized Bregman iterative method. In the second part of the paper, the proposed algorithm is further accelerated through Nestrove's accelerated scheme and parameters' reset skills. Compared with the original linearized Bregman algorithm, the accelerated algorithms have better convergent speed while avoiding selecting model parameter. Simulations on sparse recovery problems show the new algorithms really have robust parameter's selections, and improve the convergent precision at the same time.