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A modified Chambolle-Pock primal-dual algorithm for Poisson noise removal

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Abstract

In this paper, we study the Poisson noise removal problem with total variation regularization term. Using the dual formulation of total variation and Lagrange dual, we formulate the problem as a new constrained minimax problem. Then, a modified Chambolle-Pock first-order primal-dual algorithm is developed to compute the saddle point of the minimax problem. The main idea of this paper is using different step size for different primal (dual) variables updating. Moreover, the convergence of the proposed method is also established under mild conditions. Numerical comparisons between new approach and several state-of-the-art algorithms are shown to demonstrate the effectiveness of the new algorithm.

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Acknowledgements

Benxin Zhang would like to thank Professor Youwei Wen for sharing the code of the primal-dual algorithm in [13].

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Authors and Affiliations

  1. School of Electronic Engineering and Automation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Benxin Zhang & Zhijun Luo

  2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, People’s Republic of China

    Zhibin Zhu

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  1. Benxin Zhang
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Correspondence to Zhibin Zhu.

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This work is supported by the National Natural Science Foundation of China (11901137, 61967004, 11961010, 11961011), Guangxi Natural Science Foundation (2018GXNSFBA281023), Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20113), and Guangxi Key Laboratory of Cryptography and Information Security (GCIS201927).

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Zhang, B., Zhu, Z. & Luo, Z. A modified Chambolle-Pock primal-dual algorithm for Poisson noise removal. Calcolo 57, 28 (2020). https://doi.org/10.1007/s10092-020-00371-9

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  • DOI: https://doi.org/10.1007/s10092-020-00371-9

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