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Journal of Scientific Computing

, Volume 58, Issue 3, pp 548–573 | Cite as

A New Poisson Noise Filter Based on Weights Optimization

  • Qiyu Jin
  • Ion Grama
  • Quansheng LiuEmail author
Article

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.

Keywords

Poisson noise Mean Square Error Oracle estimate  Optimal Weights Filter  

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Image Processing and Pattern Recognition Shanghai Jiao Tong UniversityShanghaiChina
  2. 2.UMR 6205, Laboratoire de Mathmatiques de Bretagne AtlantiqueUniversité de Bretagne-SudVannesFrance
  3. 3.Jiangsu Engineering Center of Network Monitoring Nanjing University of Information Science and Technology NanjingChina
  4. 4.School of Mathematics and Computing Sciences Changsha University of Science and TechnologyChangshaChina

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