Reordering for improving global Arnoldi–Tikhonov method in image restoration problems

Abstract

This paper discusses the solution of large-scale linear discrete ill-posed problems arising from image restoration problems. Since the scale of the problem is usually very large, the computations with the blurring matrix can be very expensive. In this regard, we consider problems in which the coefficient matrix is the sum of Kronecker products of matrices to benefit the computation. Here, we present an alternative approach based on reordering of the image approximations obtained with the global Arnoldi–Tikhonov method. The ordering of the intensities is such that it makes the image approximation monotonic and thus minimizes the finite differences norm. We present theoretical properties of the method and numerical experiments on image restoration.