Simultaneous reconstruction and separation in a spectral CT framework

In this paper, we propose a method to simultaneously separate and reconstruct the physical components of an object observed in the context of spectral Computed Tomography (CT). Spectral CT has been made possible thansk to the technological breakthrough of X-ray hybrid pixel detectors in the last years and brings CT imaging from an anatomic to a functional biomedical imaging modality. Our contribution considers the underlying polychromatic model of the X-ray beam and combines it with a low-rank prior on the components of the object to reconstruct. The simultaneous separation and reconstruction of components is done by solving a non-convex ill-posed inverse problem. Promising results are shown on synthetic data with a simple regularization that encompasses the positivity of quantities of interest.