Bayesian Correction of Wavelet Threshold Procedures for Image De-noising

Wavelet shrinking algorithms for image de-noising replace wavelet coeecients with absolute values below a certain threshold by zero and keep or shrink the other coeecients. This is basically a local procedure, since wavelet coeecients characterize the local regularity of a function. In spite of a careful choice of the threshold, this method does not take into account the geometrical structure of an image as it is reeected by its wavelet coeecients. Therefore we introduce an a priori, geometrical model for wavelet coeecients and combine this with the local characterization of a classical threshold procedure in a Bayesian framework. In this way, we can compute for each coeecient the probability of being \suuciently clean". Problems occur because our a priori model implicitly supposes a hard-threshold procedure, that leaves the large coeecients untouched. On the other hand, most threshold selection procedures only perform well for soft-thresholding, that shrinks the large coee-cients.