An overview of nonlinear diffraction tomography within the bayesian estimation framework

Abstract

The Bayesian approach has been proven to give a common estimation structure to existing image reconstruction and restoration methods, in spite of their apparent diversity (Demoment 1989). The goal of this paper is to investigate diffraction tomography within the Bayesian estimation framework. A regularized solution to this ill-posed nonlinear inverse problem is defined as the maximum a posteriori estimate, introducing prior information on the object to reconstruct. Two equivalent formulations of this definition are available which lead to solution of a constrained or an unconstrained optimization problem to compute this solution. Different existing methods for solving this problem — such as Born Iterative Method (Wang and Chew 1989), Newton-Kantorovitch method (Joachimovicz et al. 1991), Distorted Born Iterative method (Chew and Wang 1990) and Modified Gradient method (Kleinman and van den Berg 1992) — are interpreted as algorithms to compute the defined solution. This common point of view allows an objective comparison between these methods, from the standpoint of their convergence properties and the solution they provide.