A Novel Differential T-Matrix Method for Electromagnetic Inverse Scattering Problems With Inhomogeneous Background Media

Electromagnetic inverse scattering problems (EISPs) with inhomogeneous background media are frequently encountered, wherein both dielectric and perfect electric conductor (PEC) backgrounds/scatterers (referred to as mixed boundary problems hereafter) may coexist. In this article, a novel differential T-matrix method (DT-MM) is proposed to address such problems. First, an efficient modeling method for inhomogeneous background is proposed, which solely involves the differential formulations of T-matrices characterizing the medium properties and induced multipoles, thereby introducing no additional computational burden. Second, to mitigate the nonlinearity of EISPs, a DT-MM with a contraction scheme is further proposed to effectively reduce the degree of nonlinearity by appropriately configuring a hyperparameter. The sensitivity of the hyperparameter is analyzed, and a reliable selection strategy is provided. To solve EISPs, the spectral analysis of the mapping matrix is performed, and the differential-induced multipoles are decomposed into deterministic and ambiguous parts, with the latter being solved via subspace-based optimization method (SOM). Finally, representative numerical results are presented by processing both synthetic and experimental data to validate the accuracy, robustness, and generality of the proposed method. Comparisons with state-of-the-art inversion algorithms further demonstrate the advantages of the proposed method.