An Implementable Splitting Algorithm for the l1-norm Regularized Split Feasibility Problem

The split feasibility problem (SFP) captures a wide range of inverse problems, such as signal processing, image reconstruction, and so on. Recently, applications of l(1)-norm regularization to linear inverse problems, a special case of SFP, have been received a considerable amount of attention in the signal/image processing and statistical learning communities. However, the study of the l(1)-norm regularized SFP still deserves attention, especially in terms of algorithmic issues. In this paper, we shall propose an algorithm for solving the l(1)-norm regularized SFP. More specifically, we first formulate the l(1)-norm regularized SFP as a separable convex minimization problem with linear constraints, and then introduce our splitting method, which takes advantage of the separable structure and gives rise to subproblems with closed-form solutions. We prove global convergence of the proposed algorithm under certain mild conditions. Moreover, numerical experiments on an image deblurring problem verify the efficiency of our algorithm.