A Low-Nonlinearity Approach to Inverse Scattering via an Unconventional Exploitation of the Contraction Integral Equation

The contraction integral equation model is a reformulation of the scattering equations that allows the degree of nonlinearity of the data-to-unknown relationship to be controlled through a hyperparameter. In this letter, an original method based on an unconventional exploitation of the contraction integral equation is proposed for the solution of full-wave inverse scattering problems. The approach consists of two steps. In the first step, the contraction integral equation model is inverted using a large hyperparameter, i.e., within a very low-nonlinearity regime. The aim of this step is to provide a reliable estimation of the induced contrast sources and of the target support. In the second step, the retrieved contrast sources are first used to compute the corresponding total fields. Then, the estimated fields are exploited to formulate a linear relationship between the measured data and the unknown contrast. Finally, the target properties are reconstructed by solving a properly regularized linear inverse problem, where the target support estimated in the first step can also be used to improve the result. The proposed method is validated using both synthetic and experimental data.