A fast proximal point algorithm for ℓ1-minimization problem in compressed sensing

In this paper, a fast proximal point algorithm (PPA) is proposed for solving ℓ1-minimization problem arising from compressed sensing. The proposed algorithm can be regarded as a new adaptive version of customized proximal point algorithm, which is based on a novel decomposition for the given nonsymmetric proximal matrix M. Since the proposed method is also a special case of the PPA-based contraction method, its global convergence can be established using the framework of a contraction method. Numerical results illustrate that the proposed algorithm outperforms some existing proximal point algorithms for sparse signal reconstruction.