Relaxed Alternating Minimization Algorithm for Separable Convex Programming with Applications to Imaging

Abstract

We propose a relaxed alternating minimization algorithm for solving two-block separable convex minimization problems with linear equality constraints, where one block in the objective functions is strongly convex. We prove that the proposed algorithm converges to the optimal primal-dual solution of the original problem. Furthermore, the convergence rates of the proposed algorithm in both ergodic and nonergodic senses have also been studied. We apply the proposed algorithm to solve several composite convex minimization problems arising in image denoising and evaluate the numerical performance of the proposed algorithm on a novel image denoising model. Numerical results for both artificial and real noisy images demonstrate the efficiency and effectiveness of the proposed algorithm.