2019/11/27 by Yuwei Fan, Lexing Ying, Fan, Yuwei +1 · 2 citations
Earth and Planetary Sciences · Engineering · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.1911.13202
openalex publication_date 2019/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a neural network approach for solving two classical problems in the two-dimensional inverse wave scattering: far field pattern problem and seismic imaging. The mathematical problem of inverse wave scattering is to recover the scatterer field of a medium based on the boundary measurement of the scattered wave from the medium, which is high-dimensional and nonlinear. For the far field pattern problem under the circular experimental setup, a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction. Motivated by this and filtered back-projection, we propose an effective neural network architecture for the inverse map using the recently introduced BCR-Net along with the standard convolution layers. Analogously for the seismic imaging problem, we propose a similar neural network architecture under the rectangular domain setup with a depth-dependent background velocity. Numerical results demonstrate the efficiency of the proposed neural networks.