Multiplicative regularization for contrast profile inversion

Abstract

In this paper we discuss a new type of regularization technique for the nonlinear inverse scattering problem, namely the multiplicative technique. The main advantage is that we do not have to determine the regularization parameter before the inversion process is started. We consider different norms of the total variation as regularization factor. Specifically, we investigate a weighted L2-norm, and by using an appropriate updating scheme we show that this multiplicative regularization factor does not increase the nonlinearity of the inversion problem. Numerical examples using synthetic and experimental data demonstrate the robustness of the presented method.