Image reconstruction using scattering in SPECT.

In the medical imaging technique of Single-Photon Emission Computed Tomography (SPECT), the image of a source distributed inside the patient is obtained by measuring "ballistic" photons exiting the patient and assuming a known attenuation map. In this talk we will present an extended model for SPECT, based on which we attempt to reconstruct an image of the source and attenuation maps at the same time using measurements of "ballistic" and "scattered" photons. We will present the extended model, theoretical results on the injectivity of the linearized inverse problem and numerical experiments on synthetic and real data, which are encouraging about the feasibility of this approach. This is a joint work with F. Monard, A. Osses and F. Romero.