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A New Poisson Noise Filter Based on Weights Optimization

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Abstract

We propose a new image denoising algorithm when the data is contaminated by a Poisson noise. As in the Non-Local Means filter, the proposed algorithm is based on a weighted linear combination of the observed image. But in contrast to the latter where the weights are defined by a Gaussian kernel, we propose to choose them in an optimal way. First some “oracle” weights are defined by minimizing a very tight upper bound of the Mean Square Error. For a practical application the weights are estimated from the observed image. We prove that the proposed filter converges at the usual optimal rate to the true image. Simulation results are presented to compare the performance of the presented filter with conventional filtering methods.

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Notes

  1. \(R = poissrnd(\lambda )\) generates random numbers from the Poisson distribution with mean parameter \(\lambda \).

  2. http://www.pami.sjtu.edu.cn/people/jinqy/.

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Acknowledgments

We would like to thank the reviewers for their helpful comments and remarks. The work has been partially supported by the National Natural Science Foundation of China (Grant Nos. 11101039 and 11171044), Jiangsu Engineering Center of Network Monitoring of Nanjing University of Information Science & Technology (Grant KJR1109), and Hunan Provincial Natural Science Foundation of China (Grant No. 11JJ2001).

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Authors and Affiliations

  1. Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, No. 800 Dongchuan Road, Minhang District, Shanghai, 200240, China

    Qiyu Jin

  2. UMR 6205, Laboratoire de Mathmatiques de Bretagne Atlantique, Université de Bretagne-Sud, Campus de Tohaninic, BP 573, 56017 , Vannes, France

    Qiyu Jin, Ion Grama & Quansheng Liu

  3. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Qiyu Jin

  4. School of Mathematics and Computing Sciences, Changsha University of Science and Technology, 960, 2nd Section, Wanjiali South Road, Changsha, 410004, China

    Quansheng Liu

Authors
  1. Qiyu Jin
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  2. Ion Grama
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  3. Quansheng Liu
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Correspondence to Quansheng Liu.

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Jin, Q., Grama, I. & Liu, Q. A New Poisson Noise Filter Based on Weights Optimization. J Sci Comput 58, 548–573 (2014). https://doi.org/10.1007/s10915-013-9743-7

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