Multiplicative-regularized subspace technique to solve high contrast inverse scattering problems

In this talk, we will propose a new optimization scheme for solving electromagnetic inverse scattering problems. In the inverse scattering problemthe physical properties of hidden targets, i.e., the permittivity and/or permeability can be retrieve from the measured scattering data excited by several incidences. In [1], by the MR-FFT-TSOM, the almost perfect ‘Austria’ profile, with permittivity ε
r
= 2.0, can be got. MR-FFT-TSOM has better stability and better robustness against noise in the inversion procedure and keeps the edge-preserving ability from MR. However, with the increment of contrast in the targets, the nonlinearity of the inverse scattering problem is strong and MR-FFT-TSOM maybe failure in the reconstruction. In this paper an inversion method that combines multiplicative regularization (MR) with the new integral equations (MR-NIE) proposed in [2] is presented. It can be shown that, with the adaptive MR [1], the MR-NIE can further decrease the nonlinearity of inverse scattering problems. This is due to the fact that, in the MR-FFT-TSOM, regularization scheme can provide further stability such that a more relaxed condition of constraining the current subspace being used in the optimization can be relaxed. The new reconstruction method is able to solve inverse scattering problem with stronger scatters compared to the inversion method with NIE. Numerical simulations including both inversion of synthetic data and experimental data validate the efficacy of the proposed algorithm. As shown in Fig. 1, the ‘Austria’ profile with highly relative permittivity ε
r
= 4.5, can be reconstructed well.