A Preconditioned Inexact Newton Method for Nonlinear Sparse Electromagnetic Imaging

Abstract

A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix's singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization's penalty term is reduced during the IN iterations consistently with the scheme's quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small “ripples” that are produced by the IN step, is applied to maintain the solution's sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.