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Abstract and Applied Analysis
Volume 2013, Article ID 585310, 10 pages
Research Article

Fractional-Order Total Variation Image Restoration Based on Primal-Dual Algorithm

1College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110006, China
2MESA Lab, University of California, Merced, 5200 North Lake Road, Merced, CA 95343, USA

Received 7 August 2013; Accepted 27 September 2013

Academic Editor: Dumitru Baleanu

Copyright © 2013 Dali Chen 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.


This paper proposes a fractional-order total variation image denoising algorithm based on the primal-dual method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, convergence rate, and blocky effect. The fractional-order total variation model is introduced by generalizing the first-order model, and the corresponding saddle-point and dual formulation are constructed in theory. In order to guarantee convergence rate, the primal-dual algorithm was used to solve the constructed saddle-point problem, and the final numerical procedure is given for image denoising. Finally, the experimental results demonstrate that the proposed methodology avoids the blocky effect, achieves state-of-the-art performance, and guarantees convergence rate.