The recent development of energy-resolving cameras opens the way to new types of applications and imaging systems. In this work, we consider computerized tomography (CT) with fan beam geometry and equipped with such cameras. The measured radiation is then a function of the positions of the source and detectors and of the energy of the incoming photons. Due to the Compton effect, the variations in energy (or spectrum) of the measurement are modeled in terms of scattering events leading to the so-called Compton scattering tomography (CST). We propose an analysis of the spectral data in terms of modelling and mapping properties which results in a general reconstruction strategy. Thanks to the supplementary information given by the energy, this joint CT-CST scanner makes accurate reconstructions of characteristics of the sought-for object possible for very few source positions and a small number of detectors. The general reconstruction strategy is finally validated on synthetic data via a total variation iterative scheme. We further show how the method can be extended to high energetic polychromatic radiation sources. Also illustrative, this work motivates the potential of combining conventional CT and Compton scattering imaging (CSI) with various architectures in 2D and 3D.
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