Indexed by:期刊论文

Date of Publication:2012-01-01

Journal:INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING

Included Journals:SCIE、Scopus

Volume:9

Issue:4

Page Number:907-927

ISSN No.:1705-5105

Key Words:Image restoration; total variation; fourth-order PDE; fixed point method; homotopy method; convex combination

Abstract:The Rudin, Osher, and Fatemi model [20] (ROF) for image restoration has been extensively studied due to its edge preserving capability, but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To improve the model, Lysaker, Lundervold and Tai [14] (LLT) proposed a better second-order functional suitable for restoring smooth images but it is difficult to preserve discontinuities for non-smooth images. It turns out that results from convex combinations of ROF model and LLT model can preserve the main advantages of both models (see [16, 9]). In this paper, we first propose an applicable homotopy algorithm based fixed point method for the LLT model. We then propose two new variants of convex combination models. Numerical experiments are shown to demonstrate the advantages of these combination models and the robustness of our homotopy algorithm.