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Mathematical Problems in Engineering
Volume 2011, Article ID 380807, 20 pages
Research Article

Efficient and Effective Total Variation Image Super-Resolution: A Preconditioned Operator Splitting Approach

1School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China
2Department of Information and Computing Science, Guangxi University of Technology, Liuzhou 545006, China
3Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China

Received 23 August 2010; Revised 30 November 2010; Accepted 4 January 2011

Academic Editor: J. J. Judice

Copyright © 2011 Li-Li Huang 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.


Super-resolution is a fusion process for reconstructing a high-resolution image from a set of low-resolution images. This paper proposes a novel approach to image super-resolution based on total variation (TV) regularization. We applied the Douglas-Rachford splitting technique to the constrained TV-based variational SR model which is separated into three subproblems that are easy to solve. Then, we derive an efficient and effective iterative scheme, which includes a fast iterative shrinkage/thresholding algorithm for denoising problem, a very simple noniterative algorithm for fusion part, and linear equation systems for deblurring process. Moreover, to speed up convergence, we provide an accelerated scheme based on precondition design of initial guess and forward-backward splitting technique which yields linear systems of equations with a nice structure. The proposed algorithm shares a remarkable simplicity together with a proven global rate of convergence which is significantly better than currently known lagged diffusivity fixed point iteration algorithm and fast decoupling algorithm by exploiting the alternating minimizing approach. Experimental results are presented to illustrate the effectiveness of the proposed algorithm.