Discretization and Bayesian modeling in inverse problems and imaging

Abstract

In this thesis the Bayesian modeling and discretization are studied in inverse problems related to imaging. The treatise consists of four articles which focus on the phenomena that appear when more detailed data or a priori information become available. Novel Bayesian methods for solving ill-posed signal processing problems in edge-preserving manner are introduced and analysed. Furthermore, modeling photographs in image processing problems is studied and a novel model is presented