Indexed by:期刊论文

Date of Publication:2012-03-01

Journal:APPLIED NUMERICAL MATHEMATICS

Included Journals:SCIE、EI

Volume:62

Issue:3

Page Number:185-200

ISSN No.:0168-9274

Key Words:Image denoising; Total variation; Mean curvature; Fixed point curvature method; Homotopy method

Abstract:Variational image denoising models based on regularization of gradients have been extensively studied. The total variation model by Rudin, Usher, and Fatemi (1992) [38] can preserve edges well but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To overcome this, mean curvature-based energy minimization models offer one approach for restoring both smooth (no edges) and nonsmooth (with edges) images. As such models lead to fourth order (instead of the usual second order) nonlinear partial differential equations, development of fast solvers is a challenging task. Previously stabilized fixed point methods and their associated multigrid methods were developed but the underlying operators must be regularized by a relatively large parameter. In this paper, we first present a fixed point curvature method for solving such equations and then propose a homotopy approach for varying the regularized parameter so that the Newton type method becomes applicable in a predictor-corrector framework. Numerical experiments show that both of our methods are able to maintain all important information in the image, and at the same time to filter out noise. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.