Learning the geometry of wave-based imaging

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.

Accepted as spotlight presentation to NeurIPS '20

References in corpus (10)

• Deep Convolutional Neural Network for Inverse Problems in Imaging
• Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
• On instabilities of deep learning in image reconstruction - Does AI come at a cost?
• Deep Learning Microscopy
• BCR-Net: a neural network based on the nonstandard wavelet form
• Meta-learning Pseudo-differential Operators with Deep Neural Networks
• Learning to solve inverse problems using Wasserstein loss
• Real-time photoacoustic projection imaging using deep learning
• Multi-scale discrete approximations of Fourier integral operators associated with canonical transformations and caustics
• Solving Optical Tomography with Deep Learning