Solving Strongly Nonlinear Inverse Scattering Problems for Mixture of Dielectric and PEC with Novel Contraction T-Matrix Equation

The classical inverse scattering methods have been developed to reformulate the Lippmann-Schwinger integral equation (LS-IE) for mitigating the nonlinearity, such as the new integral equation (NIE). However, LS-IE-based inversion algorithms may fail in scenarios involving mixtures of highly lossy dielectric and perfect electric conductor (PEC) scatterers. To overcome these challenges, in this article, inspired by recent advancements in NIE, a novel contraction T-matrix equation (CT-ME) with a control factor is proposed to model strongly nonlinear inverse scattering problems. By increasing the control factor, the nonlinearity of CT-ME can be progressively reduced, which is why it is referred to as a contraction transformation. Crucially, an empirical guideline for determining the optimal control factor is provided, showing that it can be flexibly and dynamically chosen from a consecutive range rather than a single value. Besides, the subspace-based optimization method (SOM) is reformulated within the CT-ME framework to solve inverse problems. Finally, representative numerical and experimental results are presented. A comparative analysis with original T-matrix equation (T-ME) further highlights the superiority of CT-ME in handling strong nonlinearity, and then, a comparison with NIE underscores the reliability of CT-ME in distinguishing PEC scatterers from highly lossy dielectric ones.