A New Poisson Noise Filter Based on Weights Optimization

Authors:
Qiyu Jin;Ion Grama;Quansheng Liu
Affiliations:
Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China 200240 and UMR 6205, Laboratoire de Mathmatiques de Bretagne Atlantique, Université de Br ...;UMR 6205, Laboratoire de Mathmatiques de Bretagne Atlantique, Université de Bretagne-Sud, Vannes, France 56017;UMR 6205, Laboratoire de Mathmatiques de Bretagne Atlantique, Université de Bretagne-Sud, Vannes, France 56017 and School of Mathematics and Computing Sciences, Changsha University of Science ...
Venue:
Journal of Scientific Computing
Year:
2014

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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.