# Solving Optical Tomography with Deep Learning

arXiv: https://arxiv.org/abs/1910.04756 · HTML: https://mlsanity.com/paper/1910.04756/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Solving the inverse problem of microscopy deconvolution with a residual Beylkin-Coifman-Rokhlin neural network](https://mlsanity.com/paper/2407.03239/) (2024)
- [GAIA: Geometry-Adaptive Operator Learning for Forward and Inverse Problems](https://mlsanity.com/paper/2607.01128/) (2026)
- [DeepRTE: Pre-trained Attention-based Neural Network for Radiative Transfer](https://mlsanity.com/paper/2505.23190/) (2025)

## Abstract (arXiv)

This paper presents a neural network approach for solving two-dimensional optical tomography (OT) problems based on the radiative transfer equation. The mathematical problem of OT is to recover the optical properties of an object based on the albedo operator that is accessible from boundary measurements. Both the forward map from the optical properties to the albedo operator and the inverse map are high-dimensional and nonlinear. For the circular tomography geometry, a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction. Motivated by this, we propose effective neural network architectures for the forward and inverse maps based on convolution layers, with weights learned from training datasets. Numerical results demonstrate the efficiency of the proposed neural networks.