Abstract

In the past, filtered backprojection has been successfully applied to the problem of reconstructing images from x-ray diffraction tomographic data; however, this technique is applicable only under conditions of low x-ray attenuation. We present a more suitable reconstruction strategy for x-ray diffraction tomography, which corrects for x-ray attenuation by using the maps of the linear attenuation coefficient that are generated by x-ray transmission computed tomography. Previously, neither the iterative reconstruction approaches nor attenuation corrections had been applied to x-ray diffraction tomographic data. A Monte Carlo simulation study of photon transport is utilized for evaluating the efficacy of the attenuation-corrected iterative reconstruction algorithm.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
    [Crossref] [PubMed]
  2. E. P. Muntz, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
    [Crossref] [PubMed]
  3. G. Harding, J. Kozanetzky, “Status and outlook of coherent x-ray scatter imaging,” J. Opt. Soc. Am. A 4, 933–944 (1987).
    [Crossref] [PubMed]
  4. G. Harding, J. Kozanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
    [Crossref] [PubMed]
  5. G. Harding, M. Newton, J. Kozanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33–41 (1990).
    [Crossref]
  6. J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
    [Crossref]
  7. H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 of The Theory of Image Formation, Detection and Processing (Academic, New York, 1981).
  8. P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).
  9. T. F. Budinger, G. T. Gullberg, R. H. Huesman, “Emission computed tomography,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 147–246.
    [Crossref]
  10. G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
    [Crossref] [PubMed]
  11. D. J. Hawkes, D. F. Jackson, “An accurate parameterisation of the x-ray attenuation coefficient,” Phys. Med. Biol. 25, 1167–1171 (1980).
    [Crossref] [PubMed]
  12. S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
    [Crossref]
  13. G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980).
  14. G. T. Herman, R. M. Lewitt, “Overview of image reconstruction from projections,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 1–7.
    [Crossref]
  15. R. Gordon, “A tutorial on ART,”IEEE Trans. Nucl. Sci. NS21, 78–93 (1974).
  16. T. Herbet, R. Leahy, M. Singh, “Three-dimensional maximum-likelihood reconstruction for an electronically collimated single-photon-emission imaging system,” J. Opt. Soc. Am. A 7, 1305–1313 (1990).
    [Crossref]
  17. J. Trampert, J. J. Leveque, “Simultaneous iterative reconstruction technique: physical interpretation based on the generalised least squares solution,”J. Geophys. Res. 95, 12, 553–12, 559 (1990).
    [Crossref]
  18. A. R. Formiconi, A. Pupi, A. Passeri, “Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique,” Phys. Med. Biol. 34, 69–84 (1989).
    [Crossref] [PubMed]
  19. S. G. Azevedo, H. E. Martz, G. P. Robertson, “Computerized tomography reconstruction technologies,” Energy and Technology Review, Nov.–Dec. 18-34 (1990); Lawrence Livermore National Laboratory Rep. UCRL-52000–90-11 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990).
  20. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).
  21. L. Eisner, I. Koltracht, P. Lancaster, “Convergence properties of ART and SOR algorithms,” Numer. Math. 59, 91–106 (1991).
    [Crossref]
  22. G. T. Herman, A. L. Lent, S. W. Rowland, “ART: mathematics and applications—a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction technique,”J. Theor. Biol. 42, 1–32 (1973).
    [Crossref] [PubMed]
  23. G. T. Herman, A. Lent, “Iterative reconstruction algorithms,” Comput. Med. Biol. 6, 273–294 (1976).
    [Crossref]
  24. F. W. Coates, G. J. Janecek, K. V. Lever, “Monte Carlo simulation and random number generation,” IEEE J. Select. Areas Commun. 6, 58–66 (1988).
    [Crossref]
  25. D. E. Raeside, “Monte Carlo principles and applications,” Phys. Med. Biol. 21, 181–197 (1976).
    [Crossref] [PubMed]
  26. D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

1993 (1)

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

1992 (1)

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

1991 (1)

L. Eisner, I. Koltracht, P. Lancaster, “Convergence properties of ART and SOR algorithms,” Numer. Math. 59, 91–106 (1991).
[Crossref]

1990 (5)

G. Harding, M. Newton, J. Kozanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33–41 (1990).
[Crossref]

S. G. Azevedo, H. E. Martz, G. P. Robertson, “Computerized tomography reconstruction technologies,” Energy and Technology Review, Nov.–Dec. 18-34 (1990); Lawrence Livermore National Laboratory Rep. UCRL-52000–90-11 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990).

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

T. Herbet, R. Leahy, M. Singh, “Three-dimensional maximum-likelihood reconstruction for an electronically collimated single-photon-emission imaging system,” J. Opt. Soc. Am. A 7, 1305–1313 (1990).
[Crossref]

J. Trampert, J. J. Leveque, “Simultaneous iterative reconstruction technique: physical interpretation based on the generalised least squares solution,”J. Geophys. Res. 95, 12, 553–12, 559 (1990).
[Crossref]

1989 (1)

A. R. Formiconi, A. Pupi, A. Passeri, “Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique,” Phys. Med. Biol. 34, 69–84 (1989).
[Crossref] [PubMed]

1988 (1)

F. W. Coates, G. J. Janecek, K. V. Lever, “Monte Carlo simulation and random number generation,” IEEE J. Select. Areas Commun. 6, 58–66 (1988).
[Crossref]

1987 (2)

G. Harding, J. Kozanetzky, “Status and outlook of coherent x-ray scatter imaging,” J. Opt. Soc. Am. A 4, 933–944 (1987).
[Crossref] [PubMed]

G. Harding, J. Kozanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

1985 (1)

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

1983 (2)

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

E. P. Muntz, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

1980 (1)

D. J. Hawkes, D. F. Jackson, “An accurate parameterisation of the x-ray attenuation coefficient,” Phys. Med. Biol. 25, 1167–1171 (1980).
[Crossref] [PubMed]

1976 (2)

D. E. Raeside, “Monte Carlo principles and applications,” Phys. Med. Biol. 21, 181–197 (1976).
[Crossref] [PubMed]

G. T. Herman, A. Lent, “Iterative reconstruction algorithms,” Comput. Med. Biol. 6, 273–294 (1976).
[Crossref]

1974 (1)

R. Gordon, “A tutorial on ART,”IEEE Trans. Nucl. Sci. NS21, 78–93 (1974).

1973 (1)

G. T. Herman, A. L. Lent, S. W. Rowland, “ART: mathematics and applications—a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction technique,”J. Theor. Biol. 42, 1–32 (1973).
[Crossref] [PubMed]

Azevedo, S. G.

S. G. Azevedo, H. E. Martz, G. P. Robertson, “Computerized tomography reconstruction technologies,” Energy and Technology Review, Nov.–Dec. 18-34 (1990); Lawrence Livermore National Laboratory Rep. UCRL-52000–90-11 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990).

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 of The Theory of Image Formation, Detection and Processing (Academic, New York, 1981).

Benci, N.

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Budinger, T. F.

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

T. F. Budinger, G. T. Gullberg, R. H. Huesman, “Emission computed tomography,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 147–246.
[Crossref]

Chen, M. H.

D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

Coates, F. W.

F. W. Coates, G. J. Janecek, K. V. Lever, “Monte Carlo simulation and random number generation,” IEEE J. Select. Areas Commun. 6, 58–66 (1988).
[Crossref]

Cullen, D. E.

D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

Davies, D. R.

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Davis, J. R.

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Eisner, L.

L. Eisner, I. Koltracht, P. Lancaster, “Convergence properties of ART and SOR algorithms,” Numer. Math. 59, 91–106 (1991).
[Crossref]

Eriksson, L.

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

Formiconi, A. R.

A. R. Formiconi, A. Pupi, A. Passeri, “Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique,” Phys. Med. Biol. 34, 69–84 (1989).
[Crossref] [PubMed]

Gordon, R.

R. Gordon, “A tutorial on ART,”IEEE Trans. Nucl. Sci. NS21, 78–93 (1974).

Grant, J. A.

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Gullberg, G. T.

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

T. F. Budinger, G. T. Gullberg, R. H. Huesman, “Emission computed tomography,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 147–246.
[Crossref]

Harding, G.

G. Harding, M. Newton, J. Kozanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33–41 (1990).
[Crossref]

G. Harding, J. Kozanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

G. Harding, J. Kozanetzky, “Status and outlook of coherent x-ray scatter imaging,” J. Opt. Soc. Am. A 4, 933–944 (1987).
[Crossref] [PubMed]

Hawkes, D. J.

D. J. Hawkes, D. F. Jackson, “An accurate parameterisation of the x-ray attenuation coefficient,” Phys. Med. Biol. 25, 1167–1171 (1980).
[Crossref] [PubMed]

Herbet, T.

Herman, G. T.

G. T. Herman, A. Lent, “Iterative reconstruction algorithms,” Comput. Med. Biol. 6, 273–294 (1976).
[Crossref]

G. T. Herman, A. L. Lent, S. W. Rowland, “ART: mathematics and applications—a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction technique,”J. Theor. Biol. 42, 1–32 (1973).
[Crossref] [PubMed]

G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980).

G. T. Herman, R. M. Lewitt, “Overview of image reconstruction from projections,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 1–7.
[Crossref]

Holte, S.

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

Hubbell, J. H.

D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

Huesman, R. H.

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

T. F. Budinger, G. T. Gullberg, R. H. Huesman, “Emission computed tomography,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 147–246.
[Crossref]

Jackson, D. F.

D. J. Hawkes, D. F. Jackson, “An accurate parameterisation of the x-ray attenuation coefficient,” Phys. Med. Biol. 25, 1167–1171 (1980).
[Crossref] [PubMed]

Janecek, G. J.

F. W. Coates, G. J. Janecek, K. V. Lever, “Monte Carlo simulation and random number generation,” IEEE J. Select. Areas Commun. 6, 58–66 (1988).
[Crossref]

Johns, P. C.

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

Koltracht, I.

L. Eisner, I. Koltracht, P. Lancaster, “Convergence properties of ART and SOR algorithms,” Numer. Math. 59, 91–106 (1991).
[Crossref]

Kozanetzky, J.

G. Harding, M. Newton, J. Kozanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33–41 (1990).
[Crossref]

G. Harding, J. Kozanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

G. Harding, J. Kozanetzky, “Status and outlook of coherent x-ray scatter imaging,” J. Opt. Soc. Am. A 4, 933–944 (1987).
[Crossref] [PubMed]

Lancaster, P.

L. Eisner, I. Koltracht, P. Lancaster, “Convergence properties of ART and SOR algorithms,” Numer. Math. 59, 91–106 (1991).
[Crossref]

Leahy, R.

Lent, A.

G. T. Herman, A. Lent, “Iterative reconstruction algorithms,” Comput. Med. Biol. 6, 273–294 (1976).
[Crossref]

Lent, A. L.

G. T. Herman, A. L. Lent, S. W. Rowland, “ART: mathematics and applications—a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction technique,”J. Theor. Biol. 42, 1–32 (1973).
[Crossref] [PubMed]

Leveque, J. J.

J. Trampert, J. J. Leveque, “Simultaneous iterative reconstruction technique: physical interpretation based on the generalised least squares solution,”J. Geophys. Res. 95, 12, 553–12, 559 (1990).
[Crossref]

Lever, K. V.

F. W. Coates, G. J. Janecek, K. V. Lever, “Monte Carlo simulation and random number generation,” IEEE J. Select. Areas Commun. 6, 58–66 (1988).
[Crossref]

Lewitt, R. M.

G. T. Herman, R. M. Lewitt, “Overview of image reconstruction from projections,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 1–7.
[Crossref]

Linden, A.

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

Malko, J. A.

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

Martz, H. E.

S. G. Azevedo, H. E. Martz, G. P. Robertson, “Computerized tomography reconstruction technologies,” Energy and Technology Review, Nov.–Dec. 18-34 (1990); Lawrence Livermore National Laboratory Rep. UCRL-52000–90-11 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990).

Morgan, M. J.

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Muntz, E. P.

E. P. Muntz, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

Neitzel, U.

G. Harding, J. Kozanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

Newton, M.

G. Harding, M. Newton, J. Kozanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33–41 (1990).
[Crossref]

Passeri, A.

A. R. Formiconi, A. Pupi, A. Passeri, “Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique,” Phys. Med. Biol. 34, 69–84 (1989).
[Crossref] [PubMed]

Pelc, N. J.

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

Perkins, S. T.

D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

Plechaty, E. F.

D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

Pupi, A.

A. R. Formiconi, A. Pupi, A. Passeri, “Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique,” Phys. Med. Biol. 34, 69–84 (1989).
[Crossref] [PubMed]

Raeside, D. E.

D. E. Raeside, “Monte Carlo principles and applications,” Phys. Med. Biol. 21, 181–197 (1976).
[Crossref] [PubMed]

Robertson, G. P.

S. G. Azevedo, H. E. Martz, G. P. Robertson, “Computerized tomography reconstruction technologies,” Energy and Technology Review, Nov.–Dec. 18-34 (1990); Lawrence Livermore National Laboratory Rep. UCRL-52000–90-11 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990).

Rosenqvist, G.

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

Rowland, S. W.

G. T. Herman, A. L. Lent, S. W. Rowland, “ART: mathematics and applications—a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction technique,”J. Theor. Biol. 42, 1–32 (1973).
[Crossref] [PubMed]

Schmidlin, P.

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

Shadbolt, P. A.

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Singh, M.

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

Suendermann, B.

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 of The Theory of Image Formation, Detection and Processing (Academic, New York, 1981).

Trampert, J.

J. Trampert, J. J. Leveque, “Simultaneous iterative reconstruction technique: physical interpretation based on the generalised least squares solution,”J. Geophys. Res. 95, 12, 553–12, 559 (1990).
[Crossref]

Wells, P.

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Yaffe, M. J.

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

Comput. Med. Biol. (1)

G. T. Herman, A. Lent, “Iterative reconstruction algorithms,” Comput. Med. Biol. 6, 273–294 (1976).
[Crossref]

Energy and Technology Review (1)

S. G. Azevedo, H. E. Martz, G. P. Robertson, “Computerized tomography reconstruction technologies,” Energy and Technology Review, Nov.–Dec. 18-34 (1990); Lawrence Livermore National Laboratory Rep. UCRL-52000–90-11 (Lawrence Livermore National Laboratory, Livermore, Calif., 1990).

IEEE J. Select. Areas Commun. (1)

F. W. Coates, G. J. Janecek, K. V. Lever, “Monte Carlo simulation and random number generation,” IEEE J. Select. Areas Commun. 6, 58–66 (1988).
[Crossref]

IEEE Trans. Nucl. Sci. (2)

S. Holte, P. Schmidlin, A. Linden, G. Rosenqvist, L. Eriksson, “Iterative image reconstruction for positron emission tomography: a study of convergence and quantitation problems,” IEEE Trans. Nucl. Sci. 37, 629–635 (1990).
[Crossref]

R. Gordon, “A tutorial on ART,”IEEE Trans. Nucl. Sci. NS21, 78–93 (1974).

J. Geophys. Res. (1)

J. Trampert, J. J. Leveque, “Simultaneous iterative reconstruction technique: physical interpretation based on the generalised least squares solution,”J. Geophys. Res. 95, 12, 553–12, 559 (1990).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Theor. Biol. (1)

G. T. Herman, A. L. Lent, S. W. Rowland, “ART: mathematics and applications—a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction technique,”J. Theor. Biol. 42, 1–32 (1973).
[Crossref] [PubMed]

Meas. Sci. Technol. (1)

J. A. Grant, M. J. Morgan, J. R. Davis, D. R. Davies, P. Wells, “X-ray diffraction microtomography,” Meas. Sci. Technol. 4, 83–87 (1993).
[Crossref]

Med. Phys. (3)

G. Harding, J. Kozanetzky, U. Neitzel, “X-ray diffraction computed tomography,” Med. Phys. 14, 515–525 (1987).
[Crossref] [PubMed]

P. C. Johns, M. J. Yaffe, “Coherent scatter in diagnostic radiology,” Med. Phys. 10, 40–50 (1983).
[Crossref] [PubMed]

E. P. Muntz, “On the significance of very small angle scattered radiation to radiographic imaging at low energies,” Med. Phys. 10, 819–823 (1983).
[Crossref] [PubMed]

Nucl. Instrum. Methods (1)

P. Wells, J. R. Davis, B. Suendermann, P. A. Shadbolt, N. Benci, J. A. Grant, D. R. Davies, M. J. Morgan, “A simple transmission X-ray microtomography instrument,” Nucl. Instrum. Methods B72, 261–270 (1992).

Numer. Math. (1)

L. Eisner, I. Koltracht, P. Lancaster, “Convergence properties of ART and SOR algorithms,” Numer. Math. 59, 91–106 (1991).
[Crossref]

Phys. Med. Biol. (5)

D. E. Raeside, “Monte Carlo principles and applications,” Phys. Med. Biol. 21, 181–197 (1976).
[Crossref] [PubMed]

G. Harding, M. Newton, J. Kozanetzky, “Energy-dispersive x-ray diffraction tomography,” Phys. Med. Biol. 35, 33–41 (1990).
[Crossref]

A. R. Formiconi, A. Pupi, A. Passeri, “Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique,” Phys. Med. Biol. 34, 69–84 (1989).
[Crossref] [PubMed]

G. T. Gullberg, R. H. Huesman, J. A. Malko, N. J. Pelc, T. F. Budinger, “An attenuated projector-backprojector for iterative SPECT reconstruction,” Phys. Med. Biol. 30, 799–816 (1985).
[Crossref] [PubMed]

D. J. Hawkes, D. F. Jackson, “An accurate parameterisation of the x-ray attenuation coefficient,” Phys. Med. Biol. 25, 1167–1171 (1980).
[Crossref] [PubMed]

Other (6)

G. T. Herman, Image Reconstruction from Projections (Academic, New York, 1980).

G. T. Herman, R. M. Lewitt, “Overview of image reconstruction from projections,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 1–7.
[Crossref]

T. F. Budinger, G. T. Gullberg, R. H. Huesman, “Emission computed tomography,” in Image Reconstruction from Projections: Implementation and Applications, G. T. Herman, ed., Vol. 32 of Topics in Applied Physics (Springer-Verlag, Berlin, 1979), pp. 147–246.
[Crossref]

H. H. Barrett, W. Swindell, Radiological Imaging, Vol. 2 of The Theory of Image Formation, Detection and Processing (Academic, New York, 1981).

D. E. Cullen, M. H. Chen, J. H. Hubbell, S. T. Perkins, E. F. Plechaty, “Tables and graphs of photon-interaction cross sections from 10eV to 100GeV derived from the LLNL evaluated photon data library,” Lawrence Livermore National Laboratory Tech. Information6, UCRL-50400 (Lawrence Livermore National Laboratory, Livermore, Calif., 1989).

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Reconstruction geometry, showing source location, S, scatter detector position, D, and detection angle, ϕ. The active region, L, corresponds to the bold line through the object, and θ labels the rotation of the uv coordinate system from the xy coordinate system.

Fig. 2
Fig. 2

Simulated and measured angular scattering probability-density functions for water at an x-ray energy of 17 keV. The simulated plot has been vertically displaced for clarity.

Fig. 3
Fig. 3

Simulated and expected attenuation of the photon beam. The simulated plot has been vertically displaced for clarity. For the purpose of demonstration, the various regions of the phantom have μ equal to 0.05, 1.3, and 3.0 cm−1, respectively, as depicted by the schematic within the figure.

Fig. 4
Fig. 4

Comparison between FBP and the basic SART algorithm: (a) sinogram of the test phantom, (b) digitized test phantom, (c) image reconstructed with FBP, (d) image reconstructed with the SART, (e) absolute value of the difference between FBP and the SART.

Fig. 5
Fig. 5

XDT images, reconstructed from tomographic data obtained from a specimen of diameter 0.7 cm. The top row shows XDT images that were obtained in the laboratory and reported previously in Ref. 6. The second row shows images that we reconstructed from simulated XDT data, using FBP. The third row presents XDT images reconstructed from the same simulated XDT data set; however, ACSART was used. The bottom row represents the multiple-scatter component of the images in the second row and was produced by performance of a subtraction between the total- and single-scatter ACSART images.

Fig. 6
Fig. 6

XDT images, reconstructed from tomographic data obtained from a specimen of 3.5-cm diameter. The top row shows images that we reconstructed from simulated XDT data, using FBP. The second row presents XDT images reconstructed from the same simulated XDT data set; however, ACSART was used. The bottom row represents the multiple-scatter component of the images in the second row and was produced by performance of a subtraction between the total- and single-scatter ACSART images. Note that the upper images, produced by FBP, suffer from a cupping artifact, which wrongly emphasizes pixel value toward the periphery of the specimen. The ACSART images, however, ameliorate this problem and produce flat average pixel value across regions of uniform composition.

Fig. 7
Fig. 7

Each bar represents the ratio between total and single scatter in the regions of water, glycerol, and oil. The figure shows that the multiple-scatter component is greater when the large phantom is scanned.

Fig. 8
Fig. 8

Profile of image pixel value throughout the central column of simulated XDT images at a detection angle of 11.5°. These profiles are presented to demonstrate how FBP, b, fails to produce constant pixel value across regions of uniform composition within the phantom. This problem worsens as the size of the phantom is enlarged, with cupping becoming most serious for the 3.5-cm-diameter phantom. By contrast, the ACSART algorithm, a, produces uniform pixel value across regions of uniform composition within the phantom, and the reconstructed pixel value is independent of specimen size.

Fig. 9
Fig. 9

Each bar represents the local image rms error in the regions of water, glycerol, and oil. The figure shows that pixel value is reconstructed with less certainty when the larger phantom is scanned.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

p ( θ , n ) = N L α ( u , v , S ) f ( u , v ) β ( u , v , D ) d v ,
α ( u , v , S ) = exp [ - S ( u , v ) μ ( l ) d l ] ,
β ( u , v , D ) = exp [ - ( u , v ) D μ ( l ) d l ] .
p j ( i ) = k = 1 K w j k ( i ) f k ,
w j k ( i ) = α j k ( i ) A j k ( i ) β j k ( i ) .
f ( i ) = f ( i ) + Δ f ( i ) ,
Δ f k ( i ) = γ j = 1 J [ p j ( i ) - q j ( i ) ] w j k ( i ) m = 1 K [ w j m ( i ) ] 2 ,
q j ( i ) = m = 1 K w j m ( i ) f m ( i ) .

Metrics