Solving Inverse Wave Scattering with Deep Learning
This work addresses inverse wave scattering for applications like seismic imaging, but it appears incremental as it adapts existing neural network methods to specific setups.
The paper tackles the high-dimensional, nonlinear inverse wave scattering problem by proposing neural network architectures for recovering scatterer fields from boundary measurements, achieving efficient numerical results.
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.