A Physics-Informed Contrast Source Inversion Learning Method for Solving Full-Wave 2-D Inverse Scattering Problems

One of the primary objectives of 2-D inverse scattering problems (ISPs) is to accurately characterize the nature of an unknown tomographic domain based on the collected scattered field data. While numerous existing iterative algorithms for ISPs have been successfully applied to reconstruct various scatterers, they are often computationally expensive and prone to becoming trapped in local minima during optimization. On the other hand, approaches that combine learning methods can solve ISPs rapidly and accurately but often lack the generality of purely data-driven methods. Therefore, achieving a balance between the generality of traditional iterative methods and the efficiency and accuracy of learning-based approaches remains a significant challenge. In this work, we introduce a physics-informed and transformer-embedded neural network with the optimization objective of the contrast source inversion (CSI) method, termed PiTCSI, to bridge this gap. The promising results demonstrate that PiTCSI achieves reconstruction quality comparable to representative methods requiring only half of the training data. By the way, the results on multiple experimental datasets demonstrate the effectiveness of the approach for reconstruction from measured scattering data.