Bayesian inversion for optical diffraction tomography

Abstract

In this paper, optical diffraction tomography is considered as a non-linear inverse scattering problem and tackled within the Bayesian estimation framework. The object under test is a man-made object known to be composed of compact regions made of a finite number of different homogeneous materials. This a priori knowledge is appropriately translated by a Gauss-Markov-Potts prior. Hence, a Gauss-Markov random field is used to model the contrast distribution whereas a hidden Potts-Markov field accounts for the compactness of the regions. First, we express the a posteriori distributions of all the unknowns and then a Gibbs sampling algorithm is used to generate samples and estimate the posterior mean of the unknowns. Some preliminary results, obtained by applying the inversion algorithm to laboratory controlled data, are presented.

Bayesian estimation with Gauss-Markov-Potts priors in optical diffraction tomography

“…At the present time, another approximation method developed for Bayesian inference problems 10 , the so-called variational Bayesian approach, is under study. It allows a much faster approximation of the posterior laws than MCMC, as it is based upon an analytic approximation of the distribution, while it keeps small the approximation error.…”

Bayesian approach with prior models which enforce sparsity in signal and image processing

“…For each of these prior models, we discuss their properties and the way to use them in a Bayesian approach resulting to many different inversion algorithms. We have applied these Bayesian algorithms in many different applications such as X-ray computed tomography [35,36], optical diffraction tomography [37][38][39], positron emission tomography [40], Microwave imaging [41,42], Sources separation [43][44][45][46], spectrometry [47,48], Hyper spectral imaging [49], super resolution [50][51][52], image fusion [53], image segmentation [54], synthetic aperture radar (SAR) imaging [29]. To save the place and be very synthetic, we did not give here any simulation results or any results on different applications of these methods.…”

Bayesian estimation with Gauss-Markov-Potts priors in optical diffraction tomography

“…sample w n from p(w|E scat , χ n−1 , z n−1 , ψ n−1 ) , 2. sample χ n from p(χ|w n , ψ n−1 , z n−1 ), 3. sample z n from p(z|χ n , ψ n−1 ), 4. sample ψ n from p(ψ|w n , χ n , E scat , z n ).…”