Wavelet domain image restoration using edge preserving prior models

We consider a wavelet-based edge preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e. edges in two dimensions or jumps in 1D). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the scale based structure of the underlying image. We demonstrate an efficient algorithm for obtaining the reconstructions from observed data and for choosing the multiple regularization parameters governing the priors.