1 Introduction

Bayesian and maximum entropy solutions are increasingly being used for the reconstruction of images from noisy and incomplete data. The Bayesian strategy seeks the image of highest probability given the data. The Bayesian target function and the likelihood are related through Bayes' rule, which includes the probability distribution of the image, also known as image prior.

During the past several years a substantial amount of work has been carried out in image reconstruction in the areas of medical tomography and in optical astronomy. In the latter case, the discovery of spherical aberration in the Hubble Space Telescope in 1990 (White & Allen 1990; Hanisch & White 1993) generated a strong effort in the image reconstruction community. Since 1988 our group has been working on the development of statistically based algorithms for Image Reconstruction (Núñez 1993; Núñez & Llacer 1991, 1993a,b, 1994, 1995a,b; Llacer & Núñez 1990; Llacer et al. 1993). In particular, we have developed Bayesian algorithms with entropy prior (FMAPE), and methods based on feasibility and cross-validation in order to compute the balancing parameter between the entropy prior and the likelihood term.

In this paper we will describe the results of our effort in the reconstruction of optical astronomy data by a Bayesian method with a space variant hyperparameter which allows different degrees of resolution in different regions of the image. Regions representing bright objects, like stars, are allowed to have hyperparameters that lead to reconstructions near Maximum Likelihood, while extended objects are segmented into regions with hyperparameters adjusted in such way that lead to featureless uncorrelated normalized residuals with mean values near 1.0 in each region. A first implementation of the algorithm will be described with the reconstruction of data from the non-refurbished Hubble Telescope.