Since the discovery of the spherical aberration problem of the Hubble Space Telescope in 1990, a substantial amount of work has been done in image restoration directed towards optical astronomy. During the past few years, we have been developing statistically based algorithms for image restoration (Núñez and Llacer 1991, Núñez and Llacer 1993, Llacer and 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. The balancing parameter defines the degree of smoothness of the solution.
Bayesian and maximum entropy solutions are increasingly being used for the restoration 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. We use entropy to define this prior probability.