Embedding Deep Learning in Inverse Scattering Problems

In this paper, we introduce a deep-learning-based framework to solve electromagnetic inverse scattering problems. This framework builds on and extends the capabilities of existing physics-based inversion algorithms. These algorithms, such as the contrast source inversion, subspace-optimization method, and their variants face a problem of getting trapped in false local minima when recovering objects with high permittivity. We propose a novel convolutional neural network architecture, termed the contrast source network, that learns the noise space components of the radiation operator. Together with the signal space components directly estimated from the data, we iteratively refine the solution and show convergence to the correct solution in cases where traditional techniques fail without any significant increase in computational time. We also propose a novel multiresolution strategy that helps in producing high resolution solutions without any significant increase in computational costs. Through extensive numerical experiments, we demonstrate the ability to recover high permittivity objects that include homogeneous, heterogeneous, and lossy scatterers.