# A new nonlocal forward model for diffuse optical tomography

## TL;DR

This paper introduces a nonlocal diffusion equation as a new forward model for diffuse optical tomography, demonstrating comparable accuracy to traditional models but with significantly improved computational efficiency through a graph-based numerical method.

## Contribution

The paper proposes a novel nonlocal diffusion model for DOT and an efficient graph-based discretization method, enhancing speed without sacrificing accuracy.

## Key findings

- NDE is quantitatively comparable to DE in accuracy.
- NDE achieves up to 64% faster computation.
- Graph-based discretization is effective across different geometries.

## Abstract

The forward model in diffuse optical tomography (DOT) describes how light propagates through a turbid medium. It is often approximated by a diffusion equation (DE) that is numerically discretized by the classical finite element method (FEM). We propose a nonlocal diffusion equation (NDE) as a new forward model for DOT, the discretization of which is carried out with an efficient graph-based numerical method (GNM). To quantitatively evaluate the new forward model, we first conduct experiments on a homogeneous slab, where the numerical accuracy of both NDE and DE is compared against the existing analytical solution. We further evaluate NDE by comparing its image reconstruction performance (inverse problem) to that of DE. Our experiments show that NDE is quantitatively comparable to DE and is up to 64% faster due to the efficient graph-based representation that can be implemented identically for geometries in different dimensions.