0TV: A New Method for Image Restoration in the Presence of Impulse Noise (Supplementary Material)

The global convergence of ADMM for convex problems was given by He and Yuan in [5] under the variation inequality framework. However, since our optimization problem is non-convex, the convergence analysis for ADMM needs additional conditions. In non-convex optimization, convergence to a stationary point (local minimum) is the best convergence property that we can hope for. By imposing some conditions, Wen et al. [8] managed to show that the sequence generated by ADMM converges to a KKT point. In this section, along a similar line, we establish the convergence property of proximal ADMM. First of all, we present the first-order KKT conditions of our 0TV optimization problem. For simplicity, we define: