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Advances in Multimedia
Volume 2014 (2014), Article ID 906464, 11 pages
Research Article

Deblurring by Solving a TVp-Regularized Optimization Problem Using Split Bregman Method

School of Computer Science and Technology, Huaibei Normal University, Huaibei 235000, China

Received 6 October 2014; Revised 28 November 2014; Accepted 1 December 2014; Published 16 December 2014

Academic Editor: Deepu Rajan

Copyright © 2014 Su Xiao. 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.


Image deblurring is formulated as an unconstrained minimization problem, and its penalty function is the sum of the error term and TVp-regularizers with . Although TVp-regularizer is a powerful tool that can significantly promote the sparseness of image gradients, it is neither convex nor smooth, thus making the presented optimization problem more difficult to deal with. To solve this minimization problem efficiently, such problem is first reformulated as an equivalent constrained minimization problem by introducing new variables and new constraints. Thereafter, the split Bregman method, as a solver, splits the new constrained minimization problem into subproblems. For each subproblem, the corresponding efficient method is applied to ensure the existence of closed-form solutions. In simulated experiments, the proposed algorithm and some state-of-the-art algorithms are applied to restore three types of blurred-noisy images. The restored results show that the proposed algorithm is valid for image deblurring and is found to outperform other algorithms in experiments.