Abstract
Hyperspectral computed tomography is a developing technique that exploits the property of materials to attenuate X-rays in different quantities depending on the specific energy. It allows to not only reconstruct the object, but also to estimate the concentration of the materials which compose it. The objective of the present study is to obtain an accurate material decomposition from noisy few-projection data. A preliminary comparative study of reconstruction methods based on material decomposition is performed, employing a phantom composed of materials with similar attenuation profiles with characteristic K-edges separated by only 2, 4 and 6 keV. It is found that a one-stage method encompassing both material decomposition and tomographic reconstruction in a single variational model performs better than a more conventional two-stage approach. It is further found that better modelling of noise through use of a weighted least-squares data fidelity improves reconstruction and material separation, as does the use total variation and L1-norm regularization.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Feng, J., et al.: Image-domain based material decomposition by multi-constraint optimization for spectral CT. IEEE Access 8, 155450–155458 (2020)
Tao, S., et al.: Material decomposition with prior knowledge aware iterative denoising (MD-PKAID). Phys. Med. Biol. 63, 195003 (2018)
Perelli, A. et al.: Regularization by denoising sub-sampled Newton method for spectral CT multi-material decomposition. Phil. Trans. R. Soc. A. 379, 20200191 (2021)
Mory, C., et al.: Comparison of five one-step reconstruction algorithms for spectral CT. Phys. Med. Biol. 63, 235001 (2018)
Gondzio, J., et al.: Material-separating regularizer for multi-energy X-ray tomography. Inverse Prob. 38, 025013 (2022)
Hu, Y. et al.: Spectral computed tomography with linearization and preconditioning. SIAM Journal on Scientific Computing. SIAM J. Sci. Comput. 41(5), S370–S380 (2019)
Jørgensen, J.S., et al.: Core imaging library part I: a versatile python framework for tomographic imaging. Phil. Trans. R. Soc. A. 379, 20200192 (2021)
Papoutsellis, E., et al.: Core imaging library - Part II: multichannel reconstruction for dynamic and spectral. Phil. Trans. R. Soc. A. 379, 20200193 (2021)
Poludniowski, G., et al.: Technical note: spekPy v2.0-a software toolkit for modeling x-ray tube spectra. Med. Phys. 48(7), 3630–3637 (2021)
Hansen, P. C., Jørgensen, J. S., Lionheart, B.: Computed tomography: algorithms, insight, and just enough theory. In: SIAM (2021)
Buzug, T. M.: Computed Tomography From Photon Statistics to Modern Cone-Beam CT. Springer, Cham (2008). https://doi.org/10.1007/978-3-540-39408-2
Resmerita, E., et al.: Joint additive Kullback-Leibler residual minimization and regularization for linear inverse problems. Math. Methods Appl. Sci. 30(13), 1527–44 (2007)
Kullback, S., et al.: On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951)
Alvarez, R.E., et al.: Energy-selective reconstructions in X-ray computerized tomography. Phys. Med. Biol. 21, 733–44 (1976)
Schlomka, J.P., et al.: Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical computed tomography. Phys. Med. Biol. 53, 4031 (2008)
Horé, A., Ziou, D.: Image quality metrics: PSNR vs. SSIM. In: 2010 20th International Conference on Pattern Recognition, pp. 2366–2369, Istanbul, Turkey (2010). https://doi.org/10.1109/ICPR.2010.579
Schmidt, T.G., et al.: A spectral CT method to directly estimate basis material maps from experimental photon-counting data. IEEE Trans. Med. Imaging 36(9), 1808–1819 (2017)
Liu, J., et al.: TICMR: total image constrained material reconstruction via nonlocal total variation regularization for spectral CT. IEEE Trans. Med. Imaging 35(12), 2578–2586 (2016)
Acknowledgements
This work was supported by the Villum Investigator grant no. 25893 and the Villum Synergy grant no. VIL50096 from The Villum Foundation, and by the ex60 project “Funds for selected research topics”. FB also acknowledges the “National Group for Scientific Computation (GNCS-INDAM)”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bevilacqua, F., Dong, Y., Jørgensen, J.S. (2023). Regularized Material Decomposition for K-edge Separation in Hyperspectral Computed Tomography. In: Calatroni, L., Donatelli, M., Morigi, S., Prato, M., Santacesaria, M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2023. Lecture Notes in Computer Science, vol 14009. Springer, Cham. https://doi.org/10.1007/978-3-031-31975-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-31975-4_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-31974-7
Online ISBN: 978-3-031-31975-4
eBook Packages: Computer ScienceComputer Science (R0)