A non-convex variational model for joint polyenergetic CT reconstruction, sensor denoising and material decomposition

Computed Tomography (CT) is widely used in engineering and medicine for imaging the interior of objects, patients, or animals. If the employed X-ray source is monoenergetic, image reconstruction essentially means the inversion of a ray transform. Typical X-ray sources are however polyenergetic (i.e. emit multiple wavelengths, each with different attenuation behaviour), and ignoring this fact may lead to artefacts such as beam hardening. An additional difficulty in some settings represents the occurrence of two different types of noise, the photon counting effect on the detector and the electronic noise generated e.g. by CCD cameras. We propose a novel variational image reconstruction model that takes both noise types and the polyenergetic source into account and moreover decomposes the reconstruction into different materials based on their different attenuation behaviour. In addition to a detailed mathematical analysis of the model we put forward a corresponding iterative algorithm including its convergence analysis. Numerical reconstructions of phantom data illustrate the feasibility of the approach.