Modulus Methods for Nonnegatively Constrained Image Restoration

Abstract

In image restoration problems, it is reasonable to add nonnegative constraints because of the physical meaning of images. In general, this problem can be expressed as a quadratic programming problem with nonnegative constraints, which results in a linear complementary problem from the KKT optimization conditions. By reformulating the linear complementary problem as implicit fixed-point equations, a class of modulus-based matrix splitting iteration methods is established. In this paper, for a better computational implementation, we present an inexact iteration process for these modulus-based methods. Convergence properties for this inexact process are analyzed, and some specific implementations for the inner iterations are presented. Numerical experiments for nonnegatively constrained image restorations are presented, and the results show that our methods are comparable and more efficient than the existing projection type methods.