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Title: The statistical mechanics of image restoration
Author: Pryce, Jonathan Michael
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1993
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Image restoration is concerned with the recovery of an 'improved' image from a corrupted picture, utilizing a prior model of the source and noise processes. We present a Bayesian derivation of the posterior probability distribution, which describes the relative probabilities that a certain image was the original source, given the corrupted picture. The ensemble of such restored images is modelled as a Markov random field (Ising spin system). Using a prior on the density of edges in the source, we obtain the cost function of Geman and Geman via information theoretic arguments. Using a combination of Monte Carlo simulation, the mean field approximation, and series expansion methods, we investigate the performance of the restoration scheme as a function of the parameters we have identified in the posterior distribution. We find phase transitions separating regions in which the posterior distribution is data-like, from regions in which it is prior-like, and we can explain these sudden changes of behaviour in terms of the relative free energies of metastable states. We construct a measure of the quality of the posterior distribution and use this to explore the way in which the appropriateness of the choice of prior affects the performance of the restoration. The data-like and prior-like characteristics of the posterior distribution indicate the regions of parameter space where the restoration scheme is effective and ineffective respectively. We examine the question of how best to use the posterior distribution to prescribe a single 'optimal' restored image. We make a detailed comparison of two different estimators to determine which better characterizes the posterior distribution. We propose that the TPM estimate, based on the mean of the posterior, is a more sensible choice than the MAP estimate (the mode of the posterior), both in principle and in practice, and we provide several practical and theoretical arguments in support.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available