Microwave tomography for breast cancer detection within a variational Bayesian approach

We consider a nonlinear inverse scattering problem where the goal is to detect breast cancer from measurements of the scattered field that results from its interaction with a known wave in the microwave frequency range. The modeling of the wave-object interaction is tackled through a domain integral representation of the electric field in a 2D-TM configuration. The inverse problem is solved in a Bayesian framework where the prior information is introduced via a Gauss-Markov-Potts model. A Variational Bayesian Approximation (VBA) technique is adapted to complex valued contrast and applied to compute the posterior estimators and reconstruct maps of both the permittivity and conductivity. Results obtained by means of this approach from synthetic data are compared with those given by a deterministic contrast source inversion method.