Nonlinear Electromagnetic Inverse Scattering Imaging Based on IN-LSQR

A nonlinear inversion scheme is proposed for electromagnetic inverse scattering imaging. It exploits inexact Newton (IN) and least square QR factorization (LSQR) methods to tackle the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem. A nonlinear model of the inverse scattering in functional form is developed. At every IN iteration, the sparse storage method is adopted to solve the storage and computational bottleneck of Fréchet derivative matrix, a large-scale sparse Jacobian matrix. Moreover, to address the slow convergence problem encountered in the inexact Newton solution via Landweber iterations, an LSQR algorithm is proposed for obtaining a better solution of the internal large-scale sparse linear equations in the IN step. Numerical results demonstrate the applicability of the proposed IN-LSQR method to quantitative inversion of scatterer electric performance parameters. Moreover, compared with the inexact Newton method based on Landweber iterations, the proposed method significantly improves the convergence rate with less computational and storage cost.