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Mathematical Problems in Engineering
Volume 2014, Article ID 731272, 10 pages
Research Article

A Fast Alternating Minimization Algorithm for Nonlocal Vectorial Total Variational Multichannel Image Denoising

Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073, China

Received 2 April 2014; Revised 20 July 2014; Accepted 5 August 2014; Published 26 August 2014

Academic Editor: Zhike Peng

Copyright © 2014 Rubing Xi 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.


The variational models with nonlocal regularization offer superior image restoration quality over traditional method. But the processing speed remains a bottleneck due to the calculation quantity brought by the recent iterative algorithms. In this paper, a fast algorithm is proposed to restore the multichannel image in the presence of additive Gaussian noise by minimizing an energy function consisting of an -norm fidelity term and a nonlocal vectorial total variational regularization term. This algorithm is based on the variable splitting and penalty techniques in optimization. Following our previous work on the proof of the existence and the uniqueness of the solution of the model, we establish and prove the convergence properties of this algorithm, which are the finite convergence for some variables and the -linear convergence for the rest. Experiments show that this model has a fabulous texture-preserving property in restoring color images. Both the theoretical derivation of the computation complexity analysis and the experimental results show that the proposed algorithm performs favorably in comparison to the widely used fixed point algorithm.