Inverse problems in imaging systems and the general Bayesian inversion frawework

TL;DR

This paper reviews inverse problems in imaging, introduces a Bayesian inversion framework with prior models like hidden Markov models, and demonstrates its effectiveness through detailed case studies and new results.

Contribution

It presents a unified Bayesian inversion framework for various ill-posed imaging inverse problems, including novel prior models and computational methods.

Findings

Bayesian framework effectively handles ill-posed inverse problems.

Compound hidden Markov models improve prior modeling.

New results demonstrate the framework's applicability to specific cases.

Abstract

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Bayesian estimation framework is presented which can handle, in a coherent way, all these problems. One of the main steps, in Bayesian inversion framework is the prior modeling of the unknowns. For this reason, a great number of such models and in particular the compound hidden Markov models are presented. Then, the main computational tools of the Bayesian estimation are briefly presented. Finally, some particular cases are studied in detail and new results are presented.