Stochastic methods for image restoration

Two important issues, computation and model evaluation, in general nonlinear image restoration are addressed. A new subset of the total, digital image space is defined, which is shown to be rich enough to include most natural images. Two of the major stochastic algorithms, the Gibbs sampler and Metropolis dynamics, are modified to operate within the restricted image space and are shown to converge to the desired global minimizers while at the same time reducing the computational demands by about an order of magnitude when the full intensity resolution is used. A model evaluation result is developed, based on the examination of local prototype patterns, which covers an important case of signal-dependent noise. The key smoothing parameter dictated by this criterion enables the restoration model to achieve optimal or near optimal performance within the class of regulation + data models balanced by this parameter. Finally, we apply these results to a particular astronomical imaging problem: recovering the structure of a dim disk hidden by a bright central star. Two approaches, nonparametric (or soft ) models using only generic smoothing constraints and semi-parametric models using more specific symmetry assumptions, are explored. Visually satisfactory results are obtained