On multiple scattering in Compton scattering tomography and its impact on fan-beam CT

The recent development of energy-resolving scintillation crystals opens the way to new types of applications and imaging systems. In the context of computerized tomography (CT), it enables to use the energy as a dimension of information supplementing the source and detector positions. It is then crucial to relate the energy measurements to the properties of Compton scattering, the dominant interaction between photons and matter. An appropriate model of the spectral data leads to the concept of Compton scattering tomography (CST). Multiple-order scattering constitutes the major difficulty of CST. It is, in general, impossible to know how many times a photon was scattered before being measured. In the literature, this nature of the spectral data has often been eluded by considering only the first-order scattering in models of the spectral data. This consideration, however, does not represent the reality as second- and higher-order scattering are a substantial part of the spectral measurement. In this work, we propose to tackle this difficulty by an analysis of the spectral data in terms of modeling and mapping properties. Due to the complexity of the multiple order scattering, we model and study the second-order scattering and extend the results to the higher orders by conjecture. The study ends up with a general reconstruction strategy based on the variations of the spectral data which is illustrated by simulations on a joint CST-CT fan beam scanner. We further show how the method can be extended to high energetic polychromatic radiation sources.