The estimation of images and random fields from sparse and/or noisy data is highly-developed, to the point where methods such as least-squares estimation, simulated annealing, and wavelet shrinkage are quite standardized. The key problem, however, is that the estimates are not a realistic version of the random field, and do not represent a typical or representative sample of the system being studied. Instead, what is often desired is that we find a random sample from the posterior distribution, a much more subtle and difficult problem than estimation. Typically this is solved using Markov-Chain Monte-Carlo / simulated annealing approaches, however these may be computationally challenging and slow to converge. In this paper we use hierarchical models to formulate a novel, fast posterior sampler.

}, keywords = {image estimation, image hierarchical posterior sampling, image sampling, least squares approximations, least-squares estimation, Markov processes, Markov-chain, Monte Carlo methods, Monte-Carlo method, noisy data, posterior distribution, random field, simulated annealing, wavelet shrinkage}, doi = {http://dx.doi.org/10.1109/ICIP.2003.1247088}, author = {P Fieguth} }