Reconstruction method for fluorescent X-Ray computed tomography by least-squares method using singular value decomposition

IEEE Transactions on Nuclear Science

Volumn 44, Issue 1, 1997, Pages 54-62

  Yuasa, Tetsuya ^a   Akiba, Masahiro ^a   Takeda, Tohoru ^a   Kazama, Masahiro ^a   Hoshino, Atsunori ^a   Watanabe, Yuki ^a   Hyodo, Kazuyuki ^a   Avraham Dilmanian, F ^a   Akatsuka, Takao ^a   Itai, Yuji ^a  

^a YAMAGATA UNIVERSITY   (Japan)

Author keywords

Computed tomography; Fluorescent X ray; Leastsquares method; Monte Carlo simulation; Singular value decomposition; Synchrotron radiation

Indexed keywords

COMPUTER SIMULATION; ELECTROMAGNETIC WAVE ATTENUATION; FLUORESCENCE; IMAGE RECONSTRUCTION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MONTE CARLO METHODS; NUMERICAL METHODS; SYNCHROTRON RADIATION; X RAY ANALYSIS;

ATTENUATION CORRECTION; FLUORESCENT X RAY COMPUTED TOMOGRAPHY (FXCT); PHANTOMS; SINGULAR VALUE DECOMPOSITION;

COMPUTERIZED TOMOGRAPHY;

EID: 0031077268     PISSN: 00189499     EISSN: None     Source Type: Journal    
DOI: 10.1109/23.554824     Document Type: Article

References (16)

1. A. lida and Y. Gohshi, "Tracer element analysis by X-ray fluorescent," Handbook on Synchrotron Radiation, vol. 4, S. Ebashi, M. Koch, and E. Rubensein, Eds. Amsterdam, North-Holland: Elsevier, 1991, pp. 307-348.
2. R. Cesareo and S. Mascarenhas, "A new tomographic device based on the detection of fluorescent X-rays," Nucl. Instrum. Mech., vol. A277, pp. 669-672, 1989.
3. P. Boisseau and L. Grodzins, "Fluorescence tomography using synchrotron radiation," Hyperfine Interactions, vol. 33, pp. 283-292, 1987.
4. T. Takeda, K. Ito, K. Kishi, T. Maeda, T. Yuasa, J. Wu, M. Kazama, K. Hyodo, T. Akatsuka, and Y. Itai, "Preliminary experiment of the fluorescent X-ray computed tomography with synchrotron radiation," Med. Imag. Tech., vol. 12, pp. 537-538, 1994.
5. T. Takeda, "Fluorescent CT with monochromatic X-rays from Tristan accumulation ring," abstract in invited poster CB2, in Proc. 13th Int. Accelerator Conf., Denton, TX, Nov. 7-10, 1994.
6. T. Takeda, T. Maeda, T. Yuasa, T. Akatsuka, K. Ito, K. Kishi, M. Kazama, K. Hyodo, and Y. Itai, "Fluorescent scanning X-ray tomog-raphy with synchrotron radiation," Rev. Sei. Instrum., vol. 66, no. 2, pp. 1471-1473, 1995.
7. T. Takeda, T. Maeda, T. Yuasa, J. Wu, T. Ito, K. Kishi, K. Hyodo, F.A. Dilmanian, T. Akatsuka, and Y. Itai, "Fluorescent scanning Xray tomographic image with monochromatic synchrotron X-ray," Med. Imag. Tech., vol. 14, no. 2, pp. 183-194, 1996.
8. T. Maeda, T. Takeda, K. Hyodo, T. Akatsuka, T. Yuasa, Y. Hiranaka, and Y. Itai, "An imaging algorithm for fluorescent scanning X-ray computed tomography," SICE, submitted (abstract in English).
9. J.P. Hogan, R.A. Gonsalves, and A. S. Krieger, "Fluorescent computer tomography: A model for correction of X-ray absorption," IEEE Trans. Nue. Sei., vol. 38, pp. 1721-1727, 1991.
10. C.L. Lawson and R.J. Hanson, "Solving least squares problem," SIAM, pp. 107-118, 1993.
11. C.W. Groetsch, "Some methodology for inverse problems," in Inverse Problems in the Mathematical Sciences. Vieweg: Wiesbaden, 1993, pp. 84-120.
12. H.-P. Chan and K. Doi, "The validity of Monte Carlo simulation in studies of scattered radiation in diagnostic radiology," Phy. Med. Biol., vol. 28, pp. 109-129, 1983.
13. J. Hubbell, W. Weigele, E. Biggs, T. Brown, T. Cromer, and R. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross sections," J. Phys. Chem. Réf. Data, vol. 4, pp. 471-616, 1975.
14. W.H. Press, S.A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C. Cambridge: Cambridge Univ. Press, 1988.
15. R.L. Branham, Scientific Data Analysis: An Introduction to Overdetermined Systems. New York: Springer-Verlag, 1990, ch. 3, pp. 34-66.
16. A.V. Lakshminarananan and A. Lent, "Methods of least squares and SIRT in reconstruction," J. Theor. Biol., vol. 76, pp. 267-295, 1979.