Variation-Based Residual Learning Method for Solving Inverse Scattering Problems

Learning-based methods have been widely applied to solve electromagnetic (EM) inverse scattering problems (ISPs). In learning-based induced current inversions, the deterministic part of the induced current is usually extracted from the measured scattered field and used as input to a neural network for predicting the total current. However, this approach relies solely on the neural network’s function approximation capability, which limits its generalization ability and accuracy. To address these limitations, this paper proposes a variation-based residual learning (VBRL) method. Starting with the deterministic current, a variational current is derived from the variation of the scattered field. This variational current is then used to update the deterministic current, providing a refined input for a neural network. To reduce the network’s fitting burden, a residual learning scheme is adopted, where only the residual part of the current is predicted. The total induced current is then obtained by summing the predicted residual current with the input current. In our implementation, both the variational operation and residual learning are encapsulated within a VBRL module, and multiple VBRL modules are cascaded to iteratively refine the solution for higher accuracy. Numerical results demonstrate that the proposed VBRL method achieves superior accuracy and generalization ability compared to existing learning-based approaches, with a comparable inversion time.