Multiresolution Reconstruction of a Corrupted Image Using the Wavelet Transform

We extend the work of Mallat on the use of wavelets in the multiresolution analysis of two-dimensional images to the situation where the unknown image has been corrupted by blur and noise. We introduce multiresolution versions of the iterated conditional modes and simulated annealing algorithms which allow the simultaneous estimation of the unknown image and also the location of discontinuities; the discontinuities may be modelled implicitly or explicitly. We compare our multiresolution algorithms with fixed resolution versions and illustrate their superiority in terms of both quality of reconstruction and computational speed using synthetic images.