ProMeSCT: A Proximal Metric Algorithm for Spectral CT

The acquisition of a set of spectral photon-counting computed tomography (spectral PC-CT) measurements aims at uncovering both the spatial and energetic characteristics of the imaged body, which widens the potential of tomography compared to classical computed tomography (CT). In the preclinical context, the use of polychromatic beams induces spectral mixing and, as a consequence, the reconstruction procedure requires specific algorithmic tools more complex than the standard ones used in CT. In this article, we propose a one-step inversion method to simultaneously separate and reconstruct the physical materials of an object observed in the context of spectral PC-CT. To do so, we carefully consider the underlying polychromatic model of the X-ray beam and combine it with a priori on the materials of the object to reconstruct. The simultaneous separation and reconstruction of materials is done by minimizing the resulting nonconvex ill-posed inverse problem. The dimensionality of the data and object materials worsens the computational complexity of the problem. We propose an efficient optimization algorithm based on a proximal forward-backward algorithm that is accelerated by a metric, which is specifically designed for spectral PC-CT. The efficiency of our method called ProMeSCT is demonstrated on results obtained on 3-D synthetic data with a simple regularization that encompasses the positivity of the quantities of interest.