# Learning the geometry of wave-based imaging

arXiv: https://arxiv.org/abs/2006.05854 · HTML: https://mlsanity.com/paper/2006.05854/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [Deep Microlocal Reconstruction for Limited-Angle Tomography](https://mlsanity.com/paper/2108.05732/) (2021)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [LoFi: Neural Local Fields for Scalable Image Reconstruction](https://mlsanity.com/paper/2411.04995/) (2024)
- [Flowers: A Warp Drive for Neural PDE Solvers](https://mlsanity.com/paper/2603.04430/) (2026)
- [Rates and architectures for learning geometrically non-trivial operators](https://mlsanity.com/paper/2512.09376/) (2025)
- [MiNO: Cotangent-bundle propagator learning for PDEs](https://mlsanity.com/paper/2608.15187/) (2026)

## Abstract (arXiv)

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.