Variational Bayesian inversion for microwave breast imaging

Leila Gharsalli; Hacheme Ayasso; Bernard Duchêne; Ali Mohammad-Djafari

doi:10.24423/cames.38

Leila Gharsalli Laboratoire des Signaux et Systèmes, Gif-sur-Yvette
Hacheme Ayasso GIPSA-Lab, Université Grenoble-Alpes, Grenoble
Bernard Duchêne Laboratoire des Signaux et Systèmes, Gif-sur-Yvette
Ali Mohammad-Djafari Laboratoire des Signaux et Systèmes, Gif-sur-Yvette

DOI: http://dx.doi.org/10.24423/cames.38

Abstract

Microwave imaging is considered as a nonlinear inverse scattering problem and tackled in a Bayesian estimation framework. The object under test (a breast affected by a tumor) is assumed to be composed of compact regions made of a restricted number of different homogeneous materials. This a priori knowledge is defined by a Gauss-Markov-Potts distribution. First, we express the joint posterior of all the unknowns; then, we present in detail the variational Bayesian approximation used to compute the estimators and reconstruct both permittivity and conductivity maps. This approximation consists of the best separable probability law that approximates the true posterior distribution in the Kullback-Leibler sense. This leads to an implicit parametric optimization scheme which is solved iteratively. Some preliminary results, obtained by applying the proposed method to synthetic data, are presented and compared with those obtained by means of the classical contrast source inversion method.

Keywords

inverse scattering, microwave imaging, breast cancer detection, Gauss-Markov-Potts prior, variational Bayesian approximation,

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