Image reconstruction of objects with time reversed fields by filtered forward-backward time-stepping method

Summary form only given. Time reversal imaging methods have received considerable attention since they yield accurate location estimate of point scatterers. Up to now, most time reversal methods have focused on detection and localization of point-like or small targets [1, 2] and not dealt with estimation of electrical parameter profile of scatterers. We have proposed a gradient based time-reversal imaging technique which can reconstruct electrical parameter distributions of the unknown object [3]. This method is based on the field equivalence principle and does not require the explicit knowledge of the incident field [4]. In this problem, the following functional of the parameters p = [εr(r),μr(r),ησ(r)] is to be minimized Q(P) = Σn=1N ∫0cT∫Ω̅ K(t)|un(p;r,t)|2drd(ct) where Ω̅ is the region exterior to the measurement surface S and T is the measurement time. The field un(p; r, t) is the solution of Maxwell equation for time reversed fields with the estimated parameters p under the n-th illumination. The quantity c is the light speed of the background. Due to the nonlinearity of the inverse scattering problem, the solution based on gradient methods often gets trapped into a local minimum. In order to avoid this problem, the filtered forwardbackward time-stepping (FBTS) technique is used [5]. In this technique, the measured total field data is processed through a low-pass filter with several cut-off frequency sequences and these filtered data are solved by FBTS method. Numerical simulations show the effectiveness of the proposed method.