Open Access
| Issue |
ESAIM: M2AN
Volume 60, Number 2, March-April 2026
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|---|---|---|
| Page(s) | 945 - 980 | |
| DOI | https://doi.org/10.1051/m2an/2026023 | |
| Published online | 17 April 2026 | |
- M. Abella, C. Martinez, M. Desco, J.J. Vaquero and J.A. Fessler, Simplified statistical image reconstruction for x-ray CT with beam-hardening artifact compensation. IEEE Trans. Med. Imaging 39 (2020) 111–118. [Google Scholar]
- J.D. Boerckel, D.E. Mason, A.M. McDermott and E. Alsberg, Microcomputed tomography: approaches and applications in bioengineering. Stem Cell Res. Ther. 5 (2014) 1–12. [Google Scholar]
- J.M. Borwein and S.B. Lindstrom, Meetings with Lambert W and other special functions in optimization and analysis. Pure Appl. Funct. Anal. 1 (2016) 361–396. [Google Scholar]
- L. Brabant, E. Pauwels, M. Dierick, D. Van Loo, M. Boone and L. Van Hoorebeke, A novel beam hardening correction method requiring no prior knowledge, incorporated in an iterative reconstruction algorithm. NDT & E Int. 51 (2012) 68–73. [Google Scholar]
- C. Brune, 4D imaging in tomography and optical nanoscopy. Ph.D. thesis, Westfalishe Wilhelms-universitat Munster (2010). [Google Scholar]
- L. Calatroni, J.C. De Los Reyes and C.-B. Schönlieb, Infimal convolution of data discrepancies for mixed noise removal. SIAM J. Imaging Sci. 10 (2017) 1196–1233. [Google Scholar]
- A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40 (2011) 120–145. [CrossRef] [Google Scholar]
- L. Condat, Fast projection onto the simplex and the l1 ball. Math. Program. 158 (2016) 575–585. [Google Scholar]
- T.S. Curry, J.E. Dowdey and R.C. MurryJr, Christensen’s Physics of Diagnostic Radiology, 4th edition. Lea and Febiger, Philadelphia (1990). [Google Scholar]
- B. De Man, J. Nuyts, P. Dupont, G. Marchal and P. Suetens, An iterative maximum-likelihood polychromatic algorithm for CT. IEEE Trans. Med. Imaging 20 (2001) 999–1008. [Google Scholar]
- S. Deng, Y. Zhu, H. Zhang, Q. Wang, P. Zhu, K. Zhang and P. Zhang, A method for material decomposition and quantification with grating based phase CT. PLoS One 16 (2021) e0245449. [Google Scholar]
- Q. Ding, Y. Long, X. Zhang and J.A. Fessler, Statistical image reconstruction using mixed Poisson-Gaussian noise model for X-ray CT. Preprint arXiv:1801.09533 (2018). [Google Scholar]
- A. Eguizabal, O. Öktem and M.U. Persson, Deep learning for material decomposition in photon-counting CT. Preprint arXiv. 2208.03360 (2022). [Google Scholar]
- I.A. Elbakri and J.A. Fessler, Statistical image reconstruction for polyenergetic x-ray computed tomography. IEEE Trans. Med. Imaging 21 (2002) 89–99. [Google Scholar]
- I.A. Elbakri and J.A. Fessler, Segmentation-free statistical image reconstruction for polyenergetic x-ray computed tomography with experimental validation. Phys. Med. Biol. 48 (2003) 2453. [Google Scholar]
- H. Gao, H. Yu, S. Osher and G. Wang, Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM). Inverse Probl. 27 (2011) 115012. [Google Scholar]
- T. Goldstein and S. Osher, The split bregman method for 11-regularized problems. SIAM J. Imaging Sci. 2 (2009) 323–343. [Google Scholar]
- C. Hamaker, K.T. Smith, D.C. Solmon and S.L. Wagner, The divergent beam X-ray transform. Rocky Mt. J. Math. 10 (1980) 253–283. [Google Scholar]
- T. Hohweiller, N. Ducros, F.C. Peyrin and B. Sixou, An ADMM algorithm for constrained material decomposition in spectral CT, in 26th European Signal Processing Conference (EUSIPCO) (2018) 71–75. [Google Scholar]
- Y. Hu, J.G. Nagy, J. Zhang and M.S. Andersen, Nonlinear optimization for mixed attenuation polyenergetic image reconstruction. Inverse Probl. 35 (2019) 064004. [Google Scholar]
- P. Jin, C.A. Bouman and K.D. Sauer, A model-based image reconstruction algorithm with simultaneous beam hardening correction for x-ray CT. IEEE Trans. Comput. Imaging 1 (2015) 200–216. [Google Scholar]
- K. Kalare, M. Bajpai, S. Sarkar and P. Munshi, Deep neural network for beam hardening artifacts removal in image reconstruction. Appl. Intell. 52 (2022) 6037–6056. [Google Scholar]
- B.J. Kis, Z. Sarnyai, R. Kákonyi, M. Erdélyi and G. Szabó, Single-energy material decomposition using x-ray path length estimation. J. Comput. Assist. Tomogr. 36 (2012) 768–777. [Google Scholar]
- G. Landi, E.L. Piccolomini and J.G. Nagy, A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis. Inverse Probl. 33 (2017) 095005. [Google Scholar]
- K. Lange, M. Bahn and R. Little, A theoretical study of some maximum likelihood algorithms for emission and transmission tomography. IEEE Trans. Med. Imaging 6 (1987) 106–114. [Google Scholar]
- A. Lanza, S. Morigi, F. Sgallari and Y.-W. Wen, Image restoration with Poisson-Gaussian mixed noise. Comput. Methods Biomech. Biomed. Eng. Imaging Vis. 2 (2014) 12–24. [Google Scholar]
- Y. Liao, Y. Wang, S. Li, J. He, D. Zeng, Z. Bian and J. Ma, Pseudo dual energy CT imaging using deep learning-based framework: basic material estimation, in Medical Imaging 2018: Physics of Medical Imaging, edited by J.Y. Lo, T.G. Schmidt and G.-H. Chen. Vol. 10573 of International Society for Optics and Photonics. SPIE (2018) 105734N. [Google Scholar]
- J. Liu and H. Gao, Material reconstruction for spectral computed tomography with detector response function. Inverse Probl. 32 (2016) 114001. [Google Scholar]
- S. Luo, H. Wu, Y. Sun, J. Li, G. Li and N. Gu, A fast beam hardening correction method incorporated in a filtered back-projection based map algorithm. Phys. Med. Biol. 62 (2017) 1810. [Google Scholar]
- A. Markoe, Analytic Tomography. Vol. 13. Cambridge University Press, Cambridge (2006). [Google Scholar]
- C.H. McCollough, S. Leng, L. Yu and J.G. Fletcher, Dual- and multi-energy CT: principles, technical approaches, and clinical applications. Radiology 276 (2015) 637–653. [Google Scholar]
- N. Menvielle, Y. Goussard, D. Orban and G. Soulez, Reduction of beam-hardening artifacts in x-ray CT, in 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference. IEEE (2005). [Google Scholar]
- D. Modgil, D.S. Rigie, Y. Wang, X. Xiao, P.A. Vargas and P.J. La Rivière, Material identification in x-ray microscopy and micro CT using multi-layer, multi-color scintillation detectors. Phys. Med. Biol. 60 (2015) 8025. [Google Scholar]
- A.M. Müller, L. Butzhammer and T. Hausotte, Implementation of a beam hardening correction method for mono material parts using a linearization technique, in International Symposium on Digital Industrial Radiology and Computed Tomography, Fürth, Germany (2019). [Google Scholar]
- J. Nuyts, B. De Man, J.A. Fessler, W. Zbijewski and F.J. Beekman, Modelling the physics in the iterative reconstruction for transmission computed tomography. Phys. Med. Biol. 58 (2013) R63. [Google Scholar]
- C. Olasz, L.G. Varga and A. Nagy, Beam hardening artifact removal by the fusion of FBP and deep neural networks, in Thirteenth International Conference on Digital Image Processing (ICDIP 2021), edited by X. Jiang and H. Fujita. Vol. 11878 of International Society for Optics and Photonics. SPIE (2021) 1187817. [Google Scholar]
- G. Papanikos, Variational image reconstruction methods for tomography PET and transmission CT with mized Poisson-Gaussian noise. Ph.D. thesis, University of Nottingham (2020). [Google Scholar]
- A. Perelli and S.A. Martin, Regularization by denoising sub-sampled Newton method for spectral CT multi-material decomposition. Philos. Trans. A Math. Phys. Eng. Sci. 379 (2021) 20200191. [Google Scholar]
- G. Perez, S. Ament, C. Gomes and M. Barlaud, Efficient projection algorithms onto the weighted l1 ball. Artif. Intell. 306 (2022) 14. [Google Scholar]
- T. Pock and A. Chambolle, Diagonal preconditioning for first order primal-dual algorithms in convex optimization, in 2011 International Conference on Computer Vision (2011) 1762–1769. [Google Scholar]
- L.I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms. Phys. D 60 (1992) 259–268. [NASA ADS] [CrossRef] [Google Scholar]
- C. Ruth and P.M. Joseph, Estimation of a photon energy spectrum for a computed tomography scanner. Med. Phys. 24 (1997) 695–702. [Google Scholar]
- Y. Saad and M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 (1986) 856–869. [CrossRef] [Google Scholar]
- A. Sawatzky, (Nonlocal) total variation in medical imaging. Ph.D. thesis, Westfalische Wilhelms-Universitat Munster (2011). [Google Scholar]
- C.O. Schirra, B. Brendel, M.A. Anastasio and E. Roessl, Spectral CT: a technology primer for contrast agent development. Contrast Media Mol. Imaging 9 (2014) 62–70. [Google Scholar]
- R. Solem, T. Dreier, I. Goncalves and M. Bech, Material decomposition in low-energy micro-CT using a dual-threshold photon counting x-ray detector. Front. Phys. 9 (2021) 673843. [Google Scholar]
- X.-C. Tai and C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model, in Scale Space and Variational Methods in Computer Vision, edited by X.-C. Tai, K. Mørken, M. Lysaker and K.-A. Lie. Springer, Berlin (2009) 502–513. [Google Scholar]
- L.N. Trefethen and D. Bau, III, Numerical Linear Algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2022). With a foreword by James G. Nagy. [Google Scholar]
- J. Wang, X. Duan and C.H. McCollough, Material Decomposition and Post-Processing: History and Basic Principles. Springer International Publishing, Cham (2022) 3–14. [Google Scholar]
- M. Wu, Q. Yang, A. Maier and R. Fahrig, A practical statistical polychromatic image reconstruction for computed tomography using spectrum binning, in Medical Imaging 2014: Physics of Medical Imaging, edited by B.R. Whiting and C. Hoeschen. SPIE (2014). [Google Scholar]
- S. Xu, A. Uneri, A.J. Khanna, J.H. Siewerdsen and J.W. Stayman, Polyenergetic known-component CT reconstruction with unknown material compositions and unknown x-ray spectra. Phys. Med. Biol. 62 (2017) 3352. [Google Scholar]
- Y. Xue, C. Luo, Y. Jiang, P. Yang, X. Hu, Q. Zhou, J. Wang, X. Hu, K. Sheng and T. Niu, Image domain multi-material decomposition using single energy CT. Phys. Med. Biol. 65 (2020) 065014. [Google Scholar]
- Y. Xue, W. Qin, C. Luo, P. Yang, Y. Jiang, T. Tsui, H. He, L. Wang, J. Qin, Y. Xie and T. Niu, Multi-material decomposition for single energy CT using material sparsity constraint. IEEE Trans. Med. Imaging 40 (2021) 1303–1318. [Google Scholar]
- C.H. Yan, R.T. Whalen, G.S. Beaupré, S.Y. Yen and S. Napel, Reconstruction algorithm for polychromatic CT imaging: application to beam hardening correction. IEEE Trans. Med. Imaging 19 (2000) 1–11. [Google Scholar]
- Q. Yang, M. Wu, A. Maier, J. Hornegger and R. Fahrig, Evaluation of Spectrum Mismatching Using Spectrum Binning for Statistical Polychromatic Reconstruction in CT. Springer, Berlin (2014) 42–47. [Google Scholar]
- Y. Yao, L. Li and Z. Chen, Dynamic-dual-energy spectral CT for improving multi-material decomposition in image-domain. Phys. Med. Biol. 64 (2019) 135006. [Google Scholar]
- J. Zhang, Y. Hu and J.G. Nagy, A scaled gradient method for digital tomographic image reconstruction. Inverse Probl. Imaging 12 (2018) 239–259. [Google Scholar]
- W. Zhao, D. Li, K. Niu, W. Qin, H. Peng and T. Niu, Robust beam hardening artifacts reduction for computed tomography using spectrum modeling. IEEE Trans. Comput. Imaging 5 (2019) 333–342. [Google Scholar]
- W. Zhao, T. Lv, P. Gao, L. Shen, X. Dai, K. Cheng, M. Jia, Y. Chen and L. Xing, A deep learning approach for dual-energy CT imaging using a single-energy CT data, in 15th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, edited S. Matej and S.D. Metzler. Vol. 11072 of International Society for Optics and Photonics. SPIE (2019) 1107222. [Google Scholar]
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