Analysis of Multiresolution Image Denoising Schemes
	Using Generalized--Gaussian and Complexity Priors

	by Pierre Moulin and Juan Liu

        University of Illinois at Urbana-Champaign
        Beckman Institute and ECE Department
	405 N. Mathews Ave., Urbana, IL 61801 


Recent research on universal and minimax wavelet shrinkage and thresholding
methods has demonstrated near--ideal estimation performance
in various asymptotic frameworks. However, image processing practice
has shown that universal thresholding methods are outperformed
by simple Bayesian estimators assuming independent wavelet coefficients
and heavy--tailed priors such as Generalized Gaussian distributions (GGDs).
In this paper, we investigate various connections between 
shrinkage methods and MAP estimation using such priors.  In particular,
we state a simple condition under which MAP estimates are sparse.
We also introduce a new family of complexity priors
based upon Rissanen's universal prior on integers.  One particular estimator
in this class outperforms conventional wavelet--based MDL estimators.
We develop analytical expressions for the shrinkage rules
implied by GGD and complexity priors.
This allows us to show the equivalence between universal hard
thresholding, MAP estimation using a very heavy--tailed GGD,
and MDL estimation using one of the new complexity priors.
Theoretical analysis supported by numerous practical experiments shows
the robustness of some of these estimates against misspecifications
of the prior -- a basic concern in image processing applications.