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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 376802, 30 pages
http://dx.doi.org/10.1155/2012/376802
Research Article

Image Restoration Based on the Hybrid Total-Variation-Type Model

1College of Mathematics and Information Science, Henan University, Kaifeng 475004, China
2Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371
3Department of Information and Computing Science, Changsha University, Changsha 410003, China

Received 18 August 2012; Accepted 15 October 2012

Academic Editor: Changbum Chun

Copyright © 2012 Baoli Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a hybrid total-variation-type model for the image restoration problem based on combining advantages of the ROF model with the LLT model. Since two -norm terms in the proposed model make it difficultly solved by using some classically numerical methods directly, we first employ the alternating direction method of multipliers (ADMM) to solve a general form of the proposed model. Then, based on the ADMM and the Moreau-Yosida decomposition theory, a more efficient method called the proximal point method (PPM) is proposed and the convergence of the proposed method is proved. Some numerical results demonstrate the viability and efficiency of the proposed model and methods.