Time-domain inverse scattering problem for two-dimensional frequency-dispersive lossy media

Abstract

A time-domain inverse scattering method for reconstruction of dispersive dielectric properties of two-dimensional (2D) lossy media based on the Debye model by using functional analysis and variational methods is developed. Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fréchet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations. Finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain (FDTD) method. Also, the first-order Tikhonov’s regularization is adopted to cope with noise and the ill-posedness of the problem. In numerical example, the presented algorithm is applied to a 2D breast model with the help of the Polak-Ribière-Polyak (PRP) conjugate gradient (CG) method, and the results demonstrate its feasibility.