A new nonlocal forward model for diffuse optical tomography
This work addresses computational efficiency in diffuse optical tomography, an incremental improvement for medical imaging applications.
The authors tackled the forward model problem in diffuse optical tomography by proposing a nonlocal diffusion equation with a graph-based numerical method, achieving comparable accuracy to the classical diffusion equation while being up to 64% faster.
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.