Removing Poisson Noise by Optimization of Weights in Non-Local Means

In this paper, we give a new algorithm to reconstruct a image from the data contaminated by the Poisson noise. Our approach is based on the weighted average of the observations in a neighborhood. But in contrast to the Non-Local means filter, instead of using weights defined by the Gaussian kernel, we use oracle weights obtained by minimizing an upper-bound on the Mean Square Error. Our theoretical results show that the weights defined by a triangular kernel are optimal and this approach makes it possible to automatically adapt the bandwidth of the kernel for every search window. To construct a computable filter the "oracle" weights are replaced by some estimates. The implementation of the proposed algorithm is straightforward. The simulations show that our approach is very competitive.