Linearization of 2D Inverse Scattering Problems Based on Reduced Order Models

By discretizing the 2D spatial differential operator and the wave parameters together, we prove that the sub-diagonals in the sparse matrix are linear with the wave parameters. With the reduced order model approach, this linearity can be used to improve the accuracy and robustness in solving inverse scattering problems. Numerical exaxmples validate this scheme and the results show a steady convergence and well-reconstructed images.