ITERATIVE WIENER FILTERS FOR IMAGE-RESTORATION

Wiener filtering is commonly used to restore linearly degraded images. To obtain results with minimum mean-squared error, there must be accurate knowledge of the covariance of the ideal image. A set of prototype images of the ideal signal is often suggested to be used for the estimation or the covariance. However, in practical situations it is unlikely that such a set of prototypes will be available, and consequently the single copy of the degraded image is often used for the covariance estimation. This leads to undesirable restored results because of the lack of proper and sufficient images for the covariance estimate. This correspondence investigates an iterative procedure, the so-called iterative Wiener filter, which successively uses the Wiener-filtered signal as an improved prototype to update the covariance estimates. The convergence properties of this iterative filter are analyzed. It has been shown that this iterative process converges to a signal which does not correspond to the minimum mean-squared-error solution. Based on the analysis, an alternate iterative filter is proposed to correct for the convergence error. The theoretical performance or the new filter has been shown to give minimum mean-squared error. However, in practical implementation when there is unavoidable error in the covariance computation, the new filter may still result in undesirable restoration. Its performance has been investigated and a number of experiments in a practical selling were conducted to demonstrate its effectiveness.