Homotopy method for a mean curvature-based denoising model

  • Authors:

  • Fenlin Yang;Ke Chen;Bo Yu

  • Affiliations:

  • School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, PR China and Department of Mathematics, Jishou University, Jishou, Hunan 416000, PR China;Centre for Mathematical Imaging Techniques and Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, United Kingdom;School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, PR China

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

Variational image denoising models based on regularization of gradients have been extensively studied. The total variation model by Rudin, Osher, 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.