Solving Phaseless Highly Nonlinear Inverse Scattering Problems With Contraction Integral Equation for Inversion

At high frequencies, phase measurement is difficult to meet the accuracy required for imaging, and it is more susceptible to noise pollution. Consequently, it is important to develop inversion models and algorithms for electromagnetic inverse scattering problems with phaseless data (PD-ISPs). Compared to the ISPs with full-data (FD-ISPs), the PD-ISPs are more nonlinear due to the lack of the phase information. Aiming at solving highly nonlinear PD-ISPs, in this article we present a contraction integral equation for inversion (CIE-I) regularized with Fourier subspace via contrast source inversion method, denoted as PD-CSI-CIE-I. Under the model of CIE-I, the nonlinearity of PD-ISPs can be effectively alleviated. In order to stabilize CIE-I, a nested optimization scheme with multi-round procedure is adopted by choosing the proper number of low-frequency components from unknown induced current spanned in the Fourier subspace. By the Fourier bases expansion of induced current, the computational cost can be further reduced. Numerical and experimental examples validate the efficiency of the proposed inversion method. Futher, it is shown that the proposed PD-CSI-CIE-I has a stronger inversion capability than the one with the Lippmann-Schwinger integral equation (LSIE) when tackling high contrast scatterers with phaseless data.