Optimized Wiener filter

Abstract

We consider using a Wiener filter for denoising a set of input signals that is degraded by additive white Gaussian noise. The Wiener filter is designed to minimize the mean square error, and it requires the knowledge of covariance of input signals and variance of the noise. The mean square error is defined as a distance between input signals and input signals estimated by the Wiener filter from noisy output signals. Although we have to infer input signals from only noisy output signals, the input signals are required for the evaluation of the mean square error. We reformulate the mean square error using noisy output signals and the covariance of the input signals. The covariance of the input signals is estimated by minimizing the mean square error. We apply our method to the case when an input signal is not generated by the assumed prior probability. In particular, we apply our method to image restoration and obtain good estimation results.