Inverse Problems / Topological sensitivity analysis in fluorescence optical tomography

Fluorescence tomography is a non-invasive imaging modality that reconstructs fluorophore distributions inside a small animal from boundary measurements of the fluorescence light. The associated inverse problem is stabilized by a priori properties or information. In this paper, cases are considered where the fluorescent inclusions are well separated from the background and have a spatially constant concentration. Under these a priori assumptions, the identification process may be formulated as a shape optimization problem, where the interface between the fluorescent inclusion and the background constitutes the unknown shape. In this paper, we focus on the computation of the so-called topological derivative for fluorescence tomography which could be used as a stand-alone tool for the reconstruction of the fluorophore distributions or as the initialization in a level-set-based method for determining the shape of the inclusions.