Detection of blood vessels within light-scattering tissues involves detection of subtle shadows as blood absorbs light. These shadows are diffuse but measurable by a set of source-detector pairs in a spatial array of sources and detectors on the tissue surface. The measured shadows can reconstruct the internal position(s) of blood vessels.
The tomographic method involves a set of Ns sources and Nd detectors such that Nsd = Ns x Nd source-detector pairs produce Nsd measurements, each interrogating the tissue with a unique perspective, i.e., a unique region of sensitivity to voxels within the tissue.
This tutorial report describes the reconstruction of the image of a blood vessel within a soft tissue based on such source-detector measurements, by solving a matrix equation using Tikhonov regularization. This is not a novel contribution, but rather a simple introduction to a well-known method, demonstrating its use in mapping blood perfusion.