Medical Microwave Imaging Using Physics-Guided Deep Learning-Part 1: The Forward Solver

Well-designed and trained deep neural networks can solve inverse electromagnetic problems much faster than conventional solvers. However, they need a physics framework to ensure producing physically correct results. Since most physics-guided deep learning inverse solvers require substantial training with numerous epochs, each involving solving a forward problem, their accuracy and efficiency are largely defined by the utilized forward solver, which becomes a bottleneck for their practical training. Thus, a fast and accurate self-supervised deep learning forward solver is presented. The solver uses a physics-based framework that divides the domain into two regions: an interior region, which includes any scatterers, and an exterior region, which represents the background medium. A hybrid loss function, incorporating Maxwell's curl equation and integral equation with the well-defined scalar background's Green's function, is employed to guide the scattered field generated from the neural network, ensuring global and local accuracy. To verify the generality of the solver, it is trained on random objects and tested on realistic models, showing high global and local metrics accuracy. For example, more than 95% of testing cases using the proposed method achieve less than 0.15 root-mean-square error in the calculated scattered field and dielectric properties of the imaged domain compared to the ground truth. In contrast, two recent deep learning methods could only realize that level of accuracy for less than 50% of the tested cases. The reported method is 97% faster than conventional solvers, enabling the development of reliable deep-learning inverse solvers.