Material Decomposition in X-ray Spectral CT Using Multiple Constraints in Image Domain
Source abstract
Abstract
X-ray spectral CT appears as a new promising imaging modality for the quantitative measurement of materials in an object, compared to conventional energy-integrating CT or dual energy CT. We consider material decomposition in spectral CT as an overcomplete ill-conditioned inverse problem. To solve the problem, we make full use of multi-dimensional nature and high correlation of multi-energy data and spatially neighboring pixels in spectral CT. Meanwhile, we also exploit the fact that material mass density has limited value. The material decomposition is then achieved by using bounded mass density, local joint sparsity and structural low-rank (DSR) in image domain. The results on numerical phantom demonstrate that the proposed DSR method leads to more accurate decomposition than usual pseudo-inverse method with singular value decomposition (SVD) and current popular sparse regularization method with l1-norm constraint.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Advanced X-ray and CT Imaging · Radiation Dose and Imaging · Electrical and Bioimpedance Tomography
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (23)
Show source-provided references
1. Faby, S., Kuchenbecker, S., Sawall, S., Simons, D., Schlemmer, H.-P., Lell, M., Kachelrieß, M.: Performance of today’s dual energy CT and future multi energy CT in virtual non-contrast imaging and in iodine quantification: a simulation study. Med. Phys. 42, 4349–4366 (2015). https://doi.org/10.1118/1.492265410.1118/1.4922654 ↗
2. Schlomka, J.P., Roessl, E., Dorscheid, R., Dill, S., Martens, G., Istel, T., Bäumer, C., Herrmann, C., Steadman, R., Zeitler, G., Livne, A., Proksa, R.: Experimental feasibility of multi-energy photon-counting K-edge imaging in pre-clinical computed tomography. Phys. Med. Biol. 53, 4031–4047 (2008). https://doi.org/10.1088/0031-9155/53/15/00210.1088/0031-9155/53/15/002 ↗
3. Roessl, E., Proksa, R.: K-edge imaging in x-ray computed tomography using multi-bin photon counting detectors. Phys. Med. Biol. 52, 4679–4696 (2007). https://doi.org/10.1088/0031-9155/52/15/02010.1088/0031-9155/52/15/020 ↗
4. Maaß, N., Sawall, S., Knaup, M., Kachelrieß, M.: Empirical multiple energy calibration (EMEC) for material-selective CT. IEEE Nucl. Sci. Symp. Conf. Rec. (2012). https://doi.org/10.1109/nssmic.2011.615381010.1109/nssmic.2011.6153810 ↗
5. Foygel Barber, R., Sidky, E.Y., Gilat Schmidt, T., Pan, X.: An algorithm for constrained one-step inversion of spectral CT data. Phys. Med. Biol. 61, 3784–3818 (2016). https://doi.org/10.1088/0031-9155/61/10/378410.1088/0031-9155/61/10/3784 ↗
6. Faby, S., Kuchenbecker, S., Simons, D., Schlemmer, H.-P., Lell, M., Kachelrieß, M.: CT calibration and dose minimization in image-based material decomposition with energy-selective detectors. Proc. SPIE Med. Imaging. 9033, 903318 (2014). https://doi.org/10.1117/12.204287710.1117/12.2042877 ↗
7. Candes, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52, 489–509 (2006). https://doi.org/10.1109/TIT.2005.86208310.1109/TIT.2005.862083 ↗
8. Donoho, D.L.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006). https://doi.org/10.1109/TIT.2006.87158210.1109/TIT.2006.871582 ↗
9. Clark, D.P., Badea, C.T.: Spectral diffusion: an algorithm for robust material decomposition of spectral CT data. Phys. Med. Biol. 59, 6445–6466 (2014). https://doi.org/10.1088/0031-9155/59/21/644510.1088/0031-9155/59/21/6445 ↗
10. Gao, H., Yu, H., Osher, S., Wang, G.: Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM). Inverse Probl. (2011). https://doi.org/10.1088/0266-5611/27/11/11501210.1088/0266-5611/27/11/115012 ↗
11. Nie, F., Huang, H., Cai, X., Ding, C.H.: Efficient and robust feature selection via joint ℓ2, 1-norms minimization. In: Lafferty, J.D., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S., Culotta, A. (eds.) Advances in Neural Information Processing Systems, pp. 1813–1821. Curran Associates, Inc., Red Hook (2010)
12. Canes, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58, 11 (2009)
13. Holt, K.M.: Total nuclear variation and Jacobian extensions of total variation for vector fields. IEEE Trans. Image Process. 23, 3975–3989 (2014). https://doi.org/10.1109/TIP.2014.233239710.1109/TIP.2014.2332397 ↗
14. Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Mach. Learn. 3, 1–122 (2010). https://doi.org/10.1561/220000001610.1561/2200000016 ↗
15. Kowalski, M.: Sparse regression using mixed norms. Appl. Comput. Harmon. Anal. 27, 303–324 (2009). https://doi.org/10.1016/j.acha.2009.05.00610.1016/j.acha.2009.05.006 ↗
16. Rao, B.D., Kreutz-Delgado, K.: An affine scaling methodology for best basis selection. IEEE Trans. Signal Process. 47, 187–200 (1999). https://doi.org/10.1109/78.73825110.1109/78.738251 ↗
17. Cai, J.-F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20, 1956–1982 (2010). https://doi.org/10.1137/08073897010.1137/080738970 ↗
18. Duvauchelle, P., Freud, N., Kaftandjian, V., Babot, D.: Computer code to simulate X-ray imaging techniques. Nucl. Instrum. Methods Phys. Res. B 170, 245–258 (2000). https://doi.org/10.1016/s0168-583x(00)00185-310.1016/s0168-583x(00)00185-3 ↗
19. Saloman, E.B., Hubbell, J.H.: X-ray attenuation coefficients (total cross sections): comparison of the experimental data base with the recommended values of Henke and the theoretical values of Scofield for energies between 0.1–100 keV, https://www.osti.gov/scitech/biblio/6965777 , (1986)10.6028/NBS.IR.86-3431 ↗
20. Vacca, R.: Regression Diagnostics—Identifying Influential Data and Sources of Collinearity. Wiley, New Jersey (1981)
21. Ding, Q., Niu, T., Zhang, X., Long, Y.: Image-domain multi-material decomposition for dual-energy CT based on prior information of material images. Med. Phys. 45, 3614–3626 (2018). https://doi.org/10.1002/mp.1300110.1002/mp.13001 ↗
22. Zhang, Y., Xi, Y., Yang, Q., Cong, W.: Spectral CT reconstruction with image sparsity and spectral mean 2, 510–523 (2016). https://doi.org/10.1109/TCI.2016.260941410.1109/TCI.2016.2609414 ↗
23. Wang, S.L., Liao, L.Z.: Decomposition method with a variable parameter for a class of monotone variational inequality problems. J. Optim. Theory Appl. 109, 415–429 (2001). https://doi.org/10.1023/A:101752262396310.1023/A:1017522623963 ↗