An admissible solution approach for diffuse optical tomography

Our goal is to characterize the space-varying absorption coefficient from observations of diffuse light propagating through tissue. Sensor array measurements from illumination with several sources leads to an inverse problem which, due to the physics and the restriction of sensors to the surface, is ill-posed and underdetermined. Accurate, reliable solutions require a priori constraints. Here we adopt an admissible solution approach, with convex constraint functions defining admissibility conditions, implemented via the ellipsoid algorithm. The joint use of measurement-model agreement, amplitude, and total variation type constraints produces more accurate reconstructions in a variety of simulation scenarios.