A novel time-domain technique for microwave tomography imaging is proposed. In the methodology three main difficulties, nonlinearity and ill-posedness of microwave imaging problem, and dispersion characteristics of breast tissues, are effectively circumvented by nonlinear optimization method, regularization technique, and introduction of a Cole-Cole model, respectively. It is preliminarily confirmed by a two-dimensional numerical example in which noise is considered. It shows that the inversion technique is feasible to detect small breast tumors. It is easy to find shallow tumors and accuracy in estimating static conductivity is best.

Dielectric properties of a variety of media,such as biological tissues,soil,and water,are frequency-dependent,which are depicted frequently by a single-pole Debye model. A three-dimensional (3-D) time-domain electromagnetic inverse scattering technique,based on functional analysis and variation method,is developed to reconstruct dispersive properties of media. Main procedures of the technique are: ① Inverse scattering problem is turned into a constrained minimization problem,according to the least squares criterion; ② Resulting problem is translated into an unconstrained minimization one,using a penalty function method;③ Closed Fréchet derivatives of Lagrange function with respect to properties are derived,based on calculus of variations; ④ Resulting problem is solved with any gradient-based algorithm. Furthermore,a first-order Tikhonov's regularization is adopted to cope with noise and ill-posedness of the problem. In numerical experiment,the technique is applied to a simple 3-D cancerous breast model,with Polak-Ribière-Polyak conjugate gradient algorithm and finite-difference time-domain method. Simulated results demonstrate preliminarily feasibility,effectiveness and robustness of the method.