Image restoration with edge-preserving regularization in wavelet domain

Image restoration is an ill posed problem and must be regularized. Usually, the difficulty of regularization is to suppress the noise but not smooth the edges. In order to preserve the edges of restored image effectively, a general wavelet-domain edge-preserving regularization scheme which is analogous to the space-domain maximum a posterior probability (MAP) estimation in Markov random field (MRF) is proposed. The corresponding solving strategy of the wavelet-domain regularization is also put forward. Several potential functions which have the ability of edge-preserving are analyzed and tested. To get rid of the Gibbs effects brought during the wavelet-domain restoration, the horizontal (or vertical) continuity in horizontal (or vertical) subband of natural image is employed in the form of an additional penalty. And, experiments are presented to verify the theoretical results.