Abstract
We consider the problem of restoring images corrupted by Poisson noise. Under the framework of maximum a posteriori estimator, the problem can be converted into a minimization problem where the objective function is composed of a Kullback-Leibler (KL)-divergence term for the Poisson noise and a total variation (TV) regularization term. Due to the logarithm function in the KL-divergence term, the non-differentiability of TV term and the positivity constraint on the images, it is not easy to design stable and efficiency algorithm for the problem. Recently, many researchers proposed to solve the problem by alternating direction method of multipliers (ADMM). Since the approach introduces some auxiliary variables and requires the solution of some linear systems, the iterative procedure can be complicated. Here we formulate the problem as two new constrained minimax problems and solve them by Chambolle-Pock’s first order primal-dual approach. The convergence of our approach is guaranteed by their theory. Comparing with ADMM approaches, our approach requires about half of the auxiliary variables and is matrix-inversion free. Numerical results show that our proposed algorithms are efficient and outperform the ADMM approach.
Original language | English |
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Pages (from-to) | 141-160 |
Number of pages | 20 |
Journal | Science China Mathematics |
Volume | 59 |
Issue number | 1 |
Early online date | 5 Nov 2015 |
DOIs | |
Publication status | Published - Jan 2016 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2015, Science China Press and Springer-Verlag Berlin Heidelberg.
Funding
This work was supported by National Natural Science Foundation of China (Grant Nos. 11361030, 11271049 and 11271049), the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (Grant Nos. CUHK400412, HKBU502814, 211911 and 12302714), Hong Kong Research Grants Council (Grant No. AoE/M-05/12), and FRGs of Hong Kong Baptist University.
Keywords
- alternating direction method of multipliers (ADMM)
- image restoration
- minimax problem
- Poisson noise
- primal-dual
- total variation (TV)