On the Kantorovich Theorem and the Regularization of Total Variation Denoising Problems

Abstract

AbstractTotal variation methods are an optimization-based approach for solving im-age restoration problems. The mathematical formulation results in an equality con-strained optimization problem, a solution which can be obtained using Newton’smethod. This note is motivated by the numerical results of an augmented Lagrangianhomotopy method for the regularization of total variation problems. The numeri-cal technique uses the regularization parameter as a homotopy parameter which isreduced. As a result, a sequence of equality constrained optimization problems issolved using Newton’s method. In this report, the convergence of an augmented La-grangian homotopy method for total variation minimization is addressed. We presenta relationship between the homotopy parameter and the radius of the Kantorovichball. Assistant Professor, Department of Mathematics, Shippensburg University, Shippensburg, PA 17257USAy Member of Technical Staff, National Institute of Standards and Technology, Gaithersburg, MD 20899-8910 USA