Variational Bayesian inversion for microwave breast imaging

Leila Gharsalli (1) , H Ayasso (2) , Bernard Duchêne (1) , Ali Mohammad-Djafari (1)

1 L2S - Laboratoire des signaux et systèmes
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

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

Domains: Engineering Sciences [physics]; Electromagnetism

Leila Gharsalli, H Ayasso, Bernard Duchêne, Ali Mohammad-Djafari. Variational Bayesian inversion for microwave breast imaging. Computer Assisted Methods in Engineering and Science, 2014, 21 (3/4), pp.199-210. ⟨hal-01211734⟩