A New Poisson Noise Filter Based on Weights Optimization

• DOI: 10.1007/s10915-013-9743-7
• Publication Date: 2013-06-20T10:58:12Z
• Authors: Qiyu Jin; Ion Grama; Quansheng Liu
• Keywords: FOS: Computer and information sciences; [STAT.AP]Statistics [stat]/Applications [stat.AP]; 02 engineering and technology; Statistics - Applications; 01 natural sciences; 510; 004; [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing; 0202 electrical engineering, electronic engineering, information engineering; Applications (stat.AP); 0101 mathematics; [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing

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 bserved image. But in contract 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.<br/>26 pages, 7 figures and 2 tables<br/>