A Neural Network Enhanced Born Approximation for Inverse Scattering

Abstract: Time-harmonic, acoustic inverse scattering concerns the ill-posed and nonlinear problem of determining the refractive index of an inaccessible, penetrable scatterer based on far field wave scattering data. When the scattering is weak, the Born approximation provides a linearized model for recovering the shape and material properties of a scatterer. We develop two neural network algorithms--Born-CNN (BCNN) and CNN-Born (CNNB)--to correct the Born approximation when the scattering is not weak. BCNN applies a post-correction to the Born reconstruction, while CNNB pre-corrects the data. Both methods leverage the Born approximation's excellent fidelity in weak scattering, while extending its applicability beyond its theoretical limits. CNNB particularly exhibits a strong generalization to noisy and absorbing scatterers. Based on numerical tests, our approach provides alternative data-driven methods for obtaining the refractive index, extending the utility of the Born approximation to regimes where the traditional method fails.