# Neural Operator Learning for Ultrasound Tomography Inversion

arXiv: https://arxiv.org/abs/2304.03297 · HTML: https://mlsanity.com/paper/2304.03297/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 8 references that are in the map.
- First posted on arXiv 6 Apr 2023.

## Builds on (most cited first, 3 of 3)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)

## Built on by (most cited first, 5 of 5)

- [Fourier Neural Operators Explained: A Practical Perspective](https://mlsanity.com/paper/2512.01421/) (2025)
- [Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning](https://mlsanity.com/paper/2506.10973/) (2025)
- [Neural Born Series Operator for Biomedical Ultrasound Computed Tomography](https://mlsanity.com/paper/2312.15575/) (2023)
- [OpenPros: A Large-Scale Dataset for Limited View Prostate Ultrasound Computed Tomography](https://mlsanity.com/paper/2505.12261/) (2025)
- [Isotropic Fourier Neural Operators](https://mlsanity.com/paper/2605.02597/) (2026)

## Abstract (arXiv)

Neural operator learning as a means of mapping between complex function spaces has garnered significant attention in the field of computational science and engineering (CS&E). In this paper, we apply Neural operator learning to the time-of-flight ultrasound computed tomography (USCT) problem. We learn the mapping between time-of-flight (TOF) data and the heterogeneous sound speed field using a full-wave solver to generate the training data. This novel application of operator learning circumnavigates the need to solve the computationally intensive iterative inverse problem. The operator learns the non-linear mapping offline and predicts the heterogeneous sound field with a single forward pass through the model. This is the first time operator learning has been used for ultrasound tomography and is the first step in potential real-time predictions of soft tissue distribution for tumor identification in beast imaging.