title: Inverse problems of combined photoacoustic and optical coherence tomography.
abstract: Optical coherence tomography (OCT) and photoacoustic tomography are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform photoacoustic tomography and OCT imaging at once. In this paper, we present a mathematical model describing the dual experiment. Because OCT is mathematically modelled by Maxwell's equations or some simplifications of it, whereas the light propagation in quantitative photoacoustics is modelled by (simplifications of) the radiative transfer equation, the first step in the derivation of a mathematical model of the dual experiment is to obtain a unified mathematical description, which in our case are Maxwell's equations. As a by-product, we therefore derive a new mathematical model of photoacoustic tomography based on Maxwell's equations. It is well known by now that without additional assumptions on the medium, it is not possible to uniquely reconstruct all optical parameters from either one of these modalities alone. We show that in the combined approach, one has additional information, compared with a single modality, and the inverse problem of reconstruction of the optical parameters becomes feasible. © 2016 The Authors.Mathematical Methods in the Applied SciencesPublished by John Wiley & Sons Ltd.
authors.affiliation: Computational Science Center University of Vienna Oskar-Morgenstern-Platz 1 Vienna A-1090 Austria.
authors.forename: Peter
authors.initials: P
authors.lastname: Elbau
authors.affiliation: Computational Science Center University of Vienna Oskar-Morgenstern-Platz 1 Vienna A-1090 Austria.
authors.forename: Leonidas
authors.initials: L
authors.lastname: Mindrinos
authors.affiliation: Computational Science Center University of Vienna Oskar-Morgenstern-Platz 1 Vienna A-1090 Austria; Johann Radon Institute for Computational and Applied Mathematics (RICAM) Altenbergerstraße 69 Linz A-4040 Austria.
authors.forename: Otmar
authors.initials: O
authors.lastname: Scherzer
keywords: hybrid imaging; optical coherence tomography; quantitative photoacoustic tomography