Probabilistic Solution of Inverse Problems

摘要

In this thesis we study the general problem of reconstructing a function, defined on a finite lattice, from a set of incomplete, noisy and/or ambiguous observations. The goal of this work is to demonstrate the generality and practical value of a probabilistic (in particular, Bayesian) approach to this problem, particularly in the context of Computer Vision. In this approach, the prior knowledge about the solution is expressed in the form of a Gibbsian probability distribution on the space of all possible functions, so that the reconstruction task in formulated as an estimation problem.