Learning the geometry of wave-based imaging

TL;DR

This paper introduces a physics-inspired deep learning architecture called FIONet for wave-based imaging, effectively capturing complex wave geometries and outperforming traditional methods especially in out-of-distribution scenarios.

Contribution

The paper develops an interpretable neural network architecture based on Fourier integral operators that models wave physics and learns the geometry of wave propagation from data.

Findings

FIONet outperforms baseline methods in various imaging inverse problems.

The architecture effectively captures space-bending wave geometries.

FIONet shows robustness in out-of-distribution tests.

Abstract

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.