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Computed Tomography (CT) is widely used in engineering and medicine forimaging the interior of objects, patients, or animals. If the employed X-raysource is monoenergetic, image reconstruction essentially means the inversionof a ray transform. Typical X-ray sources are however polyenergetic (i.e. emitmultiple wavelengths, each with different attenuation behaviour), and ignoringthis fact may lead to artefacts such as beam hardening. An additionaldifficulty in some settings represents the occurrence of two different types ofnoise, the photon counting effect on the detector and the electronic noisegenerated e.g. by CCD cameras. We propose a novel variational imagereconstruction model that takes both noise types and the polyenergetic sourceinto account and moreover decomposes the reconstruction into differentmaterials based on their different attenuation behaviour. In addition to adetailed mathematical analysis of the model we put forward a correspondingiterative algorithm including its convergence analysis. Numericalreconstructions of phantom data illustrate the feasibility of the approach.

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