Inverse scattering in a Bayesian framework: application to microwave imaging for breast cancer detection

Abstract

In this paper, we deal with a nonlinear inverse scattering problem where the goal is to detect breast cancer from measurements of the scattered field that results from the interaction between the breast and a known interrogating wave in the microwave frequency range. Modeling of the wave-object (breast) 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 prior information, which consists in the fact that the object is supposed to be composed of compact homogeneous regions made of a restricted number of different materials, is introduced via a Gauss−Markov−Potts model. As an analytic expression for the joint maximum a posteriori (MAP) estimators yields an intractable solution, an approximation of the latter is proposed. This is done by means of a variational Bayesian approximation (VBA) technique that is adapted to complex-valued contrast and applied to compute the posterior estimators, and reconstruct maps of both permittivity and conductivity of the sought object. This leads to a joint semi-supervised estimation approach, which allows us to estimate the induced currents, the contrast and all of the parameters introduced in the prior model. The method is tested on two sets of synthetic data generated in different configurations and its performances are compared to that given by a contrast source inversion technique.