  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.
