We describe here two ways to improve on recent results in image restoration using Bayes least squares estimation with local Gaussian scale mixtures (BLS-GSM) in overcomplete oriented pyramids. First one consists of allowing for a spatial adaptation of the covariance matrix defining the GSM model at each pyramid subband. This can be implemented in practice by dividing the subbands into spatial blocks. The other, more powerful, method is to generalize the GSM model to include more than one covariance matrices for each subband. The advantage of the latter method is its flexibility, as it allows for mixing Gaussian densities with different covariance matrices at every spatial location in every subband. It also allows for non-local selective processing, taking advantage of the repetition in the scene of image features that are not necessarily spatially grouped. We also describe an empirical method to adapt denoising algorithms for doing image restoration, with the only constraint on the denoising method of being applicable to non-white noise sources. Here we present mature results of the spatially adaptive method applied to denoising and deblurring, plus some estimation techniques and encouraging preliminary results of the multi-GSM concept.

Date Published: 20 September 2007
PDF: 15 pages
Proc. SPIE 6701, Wavelets XII, 67011F (20 September 2007); doi: 10.1117/12.734572

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)