Multi-frequency Neural Contrast Source Inversion for Solving Inverse Scattering Problems: 2D Cases

In this paper, we study a multi-frequency neural contrast source inversion (MF-NeuralCSI) method for addressing two-dimensional inverse scattering problems (ISPs) with multi-frequency data. MF-NeuralCSI mimics the iterative update mechanism of the multi-frequency contrast source inversion (MF-CSI) by leveraging learned parametric update functions. In each iteration, two independent convolutional neural networks (CNNs) are constructed and trained to first update contrast sources, followed by refining the contrast distributions estimated by solving least-square problems. The cost functional of MF-CSI is reformulated as an iteration-wise constraint in MF-NeuralCSI, facilitating an unsupervised learning framework that eliminates the need for total field data and contrast distributions. The multiplicative total variation (TV) regularization is also incorporated to stabilize the training process. Numerical and experimental results validate the effectiveness of MF-NeuralCSI.