Inverse Scattering Via Virtual Experiments and Contrast Source Regularization

Abstract

In microwave imaging, the linearity of the relationship between the incident and the scattered field offers the possibility of a posteriori recombining the performed scattering experiments and then to cast the underlying inverse problem with respect to the resulting, virtual, ones. The interest of such a circumstance is that properly designed virtual experiments can enforce particular and convenient conditions. In this paper, we present an application of this paradigm to the popular contrast source inversion method. In particular, we first design a set of virtual experiments capable to induce contrast sources exhibiting circular symmetries (with respect to some pivot points). Then, we devise an original and effective regularized Contrast Source Inversion (CSI) scheme, in which a penalty term is added to the usual cost functional, in order to account for the symmetry of the auxiliary unknowns. Notably, the approach does not require any a priori assumption on the unknown contrast, as it relies on the particular nature of the virtual contrast sources. Results with single frequency Fresnel experimental data are given to assess the capabilities of the proposed approach.

The Factorization Method for Virtual Experiments Based Quantitative Inverse Scattering

“…In [6][7][8][9][10][11], the design of the VE exploits the integral equation at the core of LSM. To recall this procedure, let us introduce the far-field operator [1]:…”

“…Such a virtual experiment will be driven by the excitation function i(θ, r p ) obtained from the design Eq. (9). Notably, by changing the pivot point r p , different experiments can be designed.…”

“…In a recent series of papers [6][7][8][9][10][11], it has been shown that it is possible to take advantage of the information achieved from the LSM not only to estimate the unknown target's support, but also to introduce new quantitative inversion methods. These latter are capable of retrieving the electromagnetic parameters of the unknown targets using linear approximations that hold true for non-weak scatterers [6,7], localized non-linear approximations [8] or new regularization schemes [9,10].…”

“…These latter are capable of retrieving the electromagnetic parameters of the unknown targets using linear approximations that hold true for non-weak scatterers [6,7], localized non-linear approximations [8] or new regularization schemes [9,10].…”

“…For instance, the VE can be used within the contrast source inversion method [9] or within the distorted Born method [11]. On the other hand, one of the most interesting aspects of VE is the capability of quantitatively imaging non-weak targets via linear inversion [6,7].…”