Variational Bayesian inversion for microwave imaging applied to breast cancer detection

Abstract : In this work, microwave imaging is considered as a nonlinear inverse scattering problem and tackled within a Bayesian estimation framework. The object under test (breast affected by a tumor) is supposed to be composed of compact regions made of a restricted number of different homogeneous materials. This a priori knowledge is appropriately translated by a Gauss-Markov-Potts prior. First, we express the a posteriori probability laws of all the unknowns and then the Variational Bayesian Approximation (VBA) used to compute the posterior estimators and reconstruct both permittivity and conductivity maps. This approximation consists in the best separable probability law that approximates the true posterior probability law 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 to those obtained by means of the classical contrast source inversion method.
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Leila Gharsalli, Hacheme Ayasso, Bernard Duchêne, Ali Mohammad-Djafari. Variational Bayesian inversion for microwave imaging applied to breast cancer detection. 8th International Conference on Inverse Problems in Engineering (ICIPE 2014), May 2014, Cracovie, Poland. pp.ID 5-2. ⟨hal-01103636⟩

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