Multiparametric Electromagnetic Inversion of 3-D Anisotropic Objects Embedded in Layered Media Based on Mixed $L_1$–$L_2$ Norm Regularization

In this letter, the mixed $L_1$–$L_2$ norm regularization is adopted to constrain the full-wave inversion solution of the multiparametric electromagnetic inverse scattering by the 3-D anisotropic objects. The mixed $L_1$–$L_2$ regularization term is added to the standard $L_2$ norm cost function in the framework of the Born iterative method. In each iteration, the mixed $L_1$–$L_2$ norm term is transformed into $L_2$ norm term through a weight matrix and the whole cost function is minimized by the conjugate gradient method. Numerical results show that, compared with the traditional Tikhonov $L_2$ regularization, the mixed $L_1$–$L_2$ regularization can achieve higher reconstruction accuracy without additional computational cost due to the structural similarity constraint among different model parameters.

I. Introduction

Electromagnetic (EM) inverse scattering theory has been developed rapidly in recent decades and has been widely applied in various fields, such as breast cancer diagnostics [1], nondestructive evaluation [2], through-wall imaging [3], and so on. In many full-wave inversion (FWI) application scenarios like composite laminates scattering [4], hydraulic fracture mapping [5], EM well-logging [6], and microwave device design [7], the anisotropy of the dielectric parameters must be taken into account.