Learning the geometry of wave-based imaging
This addresses imaging challenges in domains like seismology and radar by introducing a novel architecture, though it is incremental as it builds on existing Fourier integral operator theory.
The paper tackles the problem of wave-based imaging with varying background wave speeds, where conventional convolutional networks fail due to translation equivariance, and proposes FIONet, a physics-based deep learning architecture that learns the geometry of wave propagation using optimal transport, achieving significantly better performance on imaging inverse problems, especially in out-of-distribution tests.
We propose a general physics-based deep learning architecture for wave-based imaging problems. A key difficulty in imaging problems with a varying background wave speed is that the medium "bends" the waves differently depending on their position and direction. This space-bending geometry makes the equivariance to translations of convolutional networks an undesired inductive bias. We build an interpretable neural architecture inspired by Fourier integral operators (FIOs) which approximate the wave physics. FIOs model a wide range of imaging modalities, from seismology and radar to Doppler and ultrasound. We focus on learning the geometry of wave propagation captured by FIOs, which is implicit in the data, via a loss based on optimal transport. The proposed FIONet performs significantly better than the usual baselines on a number of imaging inverse problems, especially in out-of-distribution tests.