Solving Traveltime Tomography with Deep Learning

2019/11/25 by Fan, Yuwei, Ying, Lexing
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1911.11636

Abstract

This paper introduces a neural network approach for solving two-dimensional traveltime tomography (TT) problems based on the eikonal equation. The mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the medium. This inverse map is high-dimensional and nonlinear. For the circular tomography geometry, 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 proposed BCR-Net, with weights learned from training datasets. Numerical results demonstrate the efficiency of the proposed neural networks.

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