A Preconditioned Inexact Newton Method for Nonlinear Sparse Electromagnetic Imaging

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.