| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
|
|
|---|---|---|
| Page(s) | 945 - 980 | |
| DOI | https://doi.org/10.1051/m2an/2026023 | |
| Published online | 17 April 2026 | |
A non-convex variational model for joint polyenergetic ct reconstruction, sensor denoising and material decomposition
1
Department of Mathematics, University of Manchester, Manchester, UK
2
Department of Mathematics, University of Münster, Münster, Germany
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
31
August
2024
Accepted:
15
February
2026
Abstract
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.
Mathematics Subject Classification: 90C30 / 49M37 / 65K10 / 65R32 / 45Q05
Key words: Polyenergetic computed tomography / variational image reconstruction model / material decomposition / photon counting noise / electronic noise
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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