A gradient-like variational Bayesian approach: Application to microwave imaging for breast tumor detection

In this paper a nonlinear inverse scattering problem is solved by means of a variational Bayesian approach. The objective is to detect breast tumor from measurements of the scattered fields at different frequencies and for several illuminations. This inverse problem is known to be non linear and ill-posed. Thus, it needs to be regularized by introducing a priori information. Herein, prior information available on the sought object is that it is composed of a finite known number of different materials distributed in compact regions. It is accounted for by tackling the problem in a Bayesian framework. Then, the true joint posterior is approximated by a separable law by mean of a gradient-like variational Bayesian technique. The latter is adapted to complex valued contrast and used to compute the posterior estimators through a joint update of the shape parameters of the approximating marginals. Both permittivity and conductivity maps are reconstructed and the results obtained on synthetic data show a good reconstruction quality and a convergence faster than that of the classical variational Bayesian approach.