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This paper investigates a fully unsupervised statistical method for edgepreserving image restoration and compression using a spatial decompositionscheme. Smoothed maximum likelihood is used for local estimation of edge pixelsfrom mixture parametric models of local templates. For the complementary smoothpart the traditional L2-variational problem is solved in the Fourier domainwith Thin Plate Spline (TPS) regularization. It is well known that naiveFourier compression of the whole image fails to restore a piece-wise smoothnoisy image satisfactorily due to Gibbs phenomenon. Images are interpreted asrelative frequency histograms of samples from bi-variate densities where thesample sizes might be unknown. The set of discontinuities is assumed to becompletely unsupervised Lebesgue-null, compact subset of the plane in thecontinuous formulation of the problem. Proposed spatial decomposition uses awidely used topological concept, partition of unity. The decision on edge pixelneighborhoods are made based on the multiple testing procedure of Holms.Statistical summary of the final output is decomposed into two layers ofinformation extraction, one for the subset of edge pixels and the other for thesmooth region. Robustness is also demonstrated by applying the technique onnoisy degradation of clean images.

A spatio-spectral hybridization for edge preservation and noisy image restoration via local parametric mixtures and Lagrangian relaxation