The University of Edinburgh -
Division of Informatics
Forrest Hill & 80 South Bridge

MSc Thesis #92141

Title:Stochastic Image Restoration: Clean Images and Their Likelihood
Date: 1992
Abstract:The Geman and Geman formalism for stochastic image restoration is based on Bayesian statistics, in which the posterior distribution of clean images is modelled by (i) a prior distribution (which should capture the significant statistics of clean images) and (ii) by a noise-corruption process. It thereby provides an explicit description of the probability distribution of restored images. In the past, algorithms which applied this formalism have generally been restricted to finding the maximum a posteriori (MAP) estimate (or a good approximation to it) for this distribution. They used various techniques like simulated annealing, relaxation methods, neural network methods etc. The application of these techniques are, in general, non-trivial because of the complicated nature of the associated objective function. This project used Geman and Geman's formalism to explore the statistics of restored images. The simplest case of synthetic binary images which are modelled by an Ising interaction which disfavours edges was studied. The two basic questions guiding the research were: (i) is the stochastic mean image a better reconstruction than a final reconstruction image ?, (ii) what intervals in R+ contain suitable values for the arguments related to the a prior distribution, so as to produce a suitable image restoration when using an additive point noise model and four-connected neighbourhood clique function? To answer these questions, from a given clean image a corrupted image was created by flipping pixel intensities from black to white and vice-versa with some probability. Subsequently a Monte Carlo algorithm was used to generate the ensemble of restored images with an interactive display. The previous process showed (i) that it is possible to acquire a good restoration without trying to restrain the algorithm to a subset of the search space represented by the maximum a posteriori distribution used, (iii) the numeric sets over which these arguments should range is

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