  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.

Computational Physics;Machine Learning;Numerical Analysis;Numerical Analysis