Optimal noise removal using an adaptive Wiener filter based on a locally stationary Gaussian mixture distribution model for images

This paper proposes an adaptive Wiener filter (AWF) based on the Gaussian mixture distribution model (GMM) as a realization of an optimum restoration filter. The proposed method is a kind of simple adaptive WF that classifies image blocks according to their local statistical properties and selects a matched WF from a class of a priori deduced WFs. In this method, the optimum filter is realized based on the fact that the minimum mean square error filter is reduced to a WF when the image and noise signals are both Gaussian. In addition, the probability distribution function of the signals in each class can be transformed to Gaussian by using the GMM as a statistical model for the image. In order to improve the accuracy of variance estimation and to reduce the computational complexity in deducing the WFs, a universal mixture model obtained from various kinds of training images is used as the underlying mixture model. In this paper, in restoring images corrupted with white noise, the method of estimating the covariance matrices in locally stationary processes and the method of designing the mixture model are studied, and the adaptive WF is designed. Finally, simulation results show the efficiency of the proposed method compared with conventional methods.