A relaxed-PPA contraction method for sparse signal recovery

Sparse signal recovery is a topic of considerable interest, and the literature in this field is already quite immense. Many problems that arise in sparse signal recovery can be generalized as a convex programming with linear conic constraints. In this paper, we present a new proximal point algorithm (PPA) termed as relaxed-PPA (RPPA) contraction method, for solving this common convex programming. More precisely, we first reformulate the convex programming into an equivalent variational inequality (VI), and then efficiently explore its inner structure. In each step, our method relaxes the VI-subproblem to a tractable one, which can be solved much more efficiently than the original VI. Under mild conditions, the convergence of the proposed method is proved. Experiments with l ₁ analysis show that RPPA is a computationally efficient algorithm and compares favorably with the recently proposed state-of-the-art algorithms.