A Hybrid Regularization Technique for Solving Highly Nonlinear Inverse Scattering Problems

Solving inverse scattering problems (ISPs) for targets with high contrasts and/or large dimensions suffer from severe ill-posedness and strong nonlinearity. Recently, a family of new integral equations (NIE) has been proposed to tackle such problems, in which the multiple scattering effects in estimating contrasts during inversions are suppressed by the local wave effects. This effectively reduces the nonlinearity of ISPs by transforming the problems into a new form. As in most inversions, to achieve better (stabler and faster) inversion efficiency, proper regularization techniques are needed. This paper provides the detailed studies on the two different types of regularization techniques in the inversions with the NIE, i.e., the twofold subspace-based optimization method, directly applied in the modeling, and the total variation type multiplicative regularization, conventionally applied on the unknowns. We will show that how each regularization works with the NIE and how they work together with the NIE to obtain the better performance in terms of reducing the nonlinearity and increasing the stability of the inversions. Numerical tests against synthetic data and experimental data are provided to verify the interests.