Poisson Wiener filtering with non-local weighted parameter estimation using stochastic distances

Abstract

The Wiener filter is a classical approach for signal denoising and it is known to be the optimum filter in the sense of the linear minimum mean square error (LMMSE). In general, knowledge of some statistical parameters of the underlying signal and noise are required to compute the Wiener filter. These parameters are usually estimated from the corrupted image using a local neighborhood, thus assuming that the signal and noise are locally stationary. However, images corrupted by signal-dependent noise, such as Poisson noise, are not locally stationary. In this paper, we are proposing a novel Wiener filtering approach for Poisson corrupted images considering a non-local weighted parameter estimation. In the proposed method, named Poisson Non-Local Wiener filter (PNL-Wiener), filtering parameters are estimated from the degraded image considering a non-local neighborhood, where the weights of the estimation function are computed based on the stochastic distances between image patches. Experimental results show that the proposed method is competitive to other state-of-the-art denoising methods designed specifically for Poisson corrupted images, yet providing better preservation of edges and fine details in the images.