Multiscale adaptive image restoration in the wavelet domain

This paper introduces a method for spatially adaptive image restoration based on the detail coefficients of the wavelet transform of a noisy blurred image. A multiscale recursive smoothing filter is applied to the wavelet coefficients ordered onto quadtree structures along different orientations. These coefficients are first prefiltered by a constrained least squares filter in order to remove the spatial correlations due to the blur. An optimal way of choosing the regularization parameters used for this prefiltering operation is introduced here. This is based on an analysis of the detection operations performed by the multiscale filter in order to model edge and non-edge regions of the image differently. Results show that this approach offers a highly adaptive means of preserving edges in a restored image.