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Journal of Applied Mathematics
Volume 2013, Article ID 797239, 14 pages
Research Article

Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising

1Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
2Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Received 17 October 2012; Accepted 24 January 2013

Academic Editor: Changbum Chun

Copyright © 2013 Yuying Shi and Qianshun Chang. 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.


A new deblurring and denoising algorithm is proposed, for isotropic total variation-based image restoration. The algorithm consists of an efficient solver for the nonlinear system and an acceleration strategy for the outer iteration. For the nonlinear system, the split Bregman method is used to convert it into linear system, and an algebraic multigrid method is applied to solve the linearized system. For the outer iteration, we have conducted formal convergence analysis to determine an auxiliary linear term that significantly stabilizes and accelerates the outer iteration. Numerical experiments demonstrate that our algorithm for deblurring and denoising problems is efficient.