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A Fast Algorithm for Deconvolution and Poisson Noise Removal

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Abstract

Poisson noise removal problems have attracted much attention in recent years. The main aim of this paper is to study and propose an alternating minimization algorithm for Poisson noise removal with nonnegative constraint. The algorithm minimizes the sum of a Kullback-Leibler divergence term and a total variation term. We derive the algorithm by utilizing the quadratic penalty function technique. Moreover, the convergence of the proposed algorithm is also established under very mild conditions. Numerical comparisons between our approach and several state-of-the-art algorithms are presented to demonstrate the efficiency of our proposed algorithm.

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Acknowledgements

The authors are grateful to the anonymous referees for their careful reading of this paper and their valuable suggestions, which have helped improve the quality of this paper substantially. The authors would also like to thank Professor You-Wei Wen for sending us the code of the primal dual algorithm in [45].

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Xiongjun Zhang

  2. Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Michael K. Ng

  3. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Minru Bai

Authors
  1. Xiongjun Zhang
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  2. Michael K. Ng
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  3. Minru Bai
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Corresponding author

Correspondence to Xiongjun Zhang.

Additional information

Xiongjun Zhang: The research of this author was supported in part by the Fundamental Research Funds for the Central Universities under Grant 230-20205170463-610.

Michael K. Ng: The research of this author was supported in part by the HKRGC GRF 1202715, 12306616, 12200317 and HKBU RC-ICRS/16-17/03.

Minru Bai: The research of this author was supported in part by the National Science Foundation of China under Grant 11571098.

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Zhang, X., Ng, M.K. & Bai, M. A Fast Algorithm for Deconvolution and Poisson Noise Removal. J Sci Comput 75, 1535–1554 (2018). https://doi.org/10.1007/s10915-017-0597-2

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  • DOI: https://doi.org/10.1007/s10915-017-0597-2

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