Wavelet-based approach to adaptive Wiener filtering of images in the presence of colored noise

Abstract

An adaptive Wiener filtering approach, based on image estimation in the wavelet domain, is proposed. Gradient-based estimation of the image is employed by minimizing an error functional that depends on estimates of the image and the power of the noise in each wavelet subband. The power of the noise is estimated from the variance of wavelet coefficients. The Wiener filter used in restoring the corrupted image is updated at each iteration step. Hard wavelet thresholding allows for appropriate selection of initial estimates of the restored image and the noise. The initial estimate of the restored image is then improved by updating these estimates iteratively. Conditions for convergence of the proposed procedure are derived. Experimental results for restoring images corrupted by colored noise are presented as well. Comparisons with conventional restoration techniques strongly favor the proposed method.