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 regularized inverse Born approximation provides a linearized model for recovering the shape and material properties of a scatterer. We propose two convolutional neural network (CNN) algorithms to correct the traditional inverse Born approximation even when the scattering is not weak. These are denoted Born-CNN (BCNN) and CNN-Born (CNNB). 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 more complex out of distribution scatterers. Based on numerical tests and benchmarking against other standard approaches, our corrected Born models provide alternative data-driven methods for obtaining the refractive index, extending the utility of the Born approximation to regimes where the traditional method fails.
Inverse scattering beyond Born approximation via rotation-equivariance-aware neural network and low-rank structure
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Department of Mathematical Sciences, The University of Texas at Dallas（德克萨斯大学达拉斯分校数学系）
