Abstract

In cone-beam computed tomography (CBCT), the volumetric reconstruction may in principle assume an arbitrarily fine grid. The supergridded cone-beam reconstruction refers to reconstructing the object domain or a subvolume thereof with a grid that is finer than the proper computed tomography sampling grid (as determined by gantry geometry and detector discreteness). This technique can naturally reduce the voxelization effect, thereby retaining more details for object reproduction. The grid refinement is usually limited to two or three refinement levels because the detail pursuit is eventually limited by the detector discreteness. The volume reconstruction is usually targeted to a local volume of interest due to the cubic growth in a three-dimensional (3D) array size. As an application, we used this technique for 3D point-spread function (PSF) measurement of a CBCT system by reconstructing edge spread profiles in a refined grid. Through an experiment with a Teflon ball on a CBCT system, we demonstrated the supergridded volume reconstruction (based on a Feldcamp algorithm) and the CBCT PSF measurement (based on an edge-blurring technique). In comparison with a postreconstruction image refinement technique (upsampling and interpolation), the supergridded reconstruction could produce better PSFs (in terms of a smaller FWHM and PSF fitting error).

© 2005 Optical Society of America

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References

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  1. R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
    [CrossRef] [PubMed]
  2. R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
    [CrossRef] [PubMed]
  3. Z. Chen, R. Ning, “Three-dimensional PSF measurement of cone-beam CT system by iterative edge-blurring algorithm,” Phys. Med. Biol. 49, 1865–1880 (2004).
    [CrossRef] [PubMed]
  4. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).
  5. Z. Chen, R. Ning, “Pixel-pyramid model for divergent projection geometry,” Opt. Eng. 44, 027002-1-10 (2005).
    [CrossRef]
  6. Z. Chen, R. Ning, D. Conover, “Accurate perspective projection calculation using a pixel-pyramid model for iterative cone-beam reconstruction,” in Physics of Medical Imaging, M. Yaffe, L. Antonuk, eds., Proc. SPIE5030, 728–739 (2003).
  7. L. A. Feldkamp, L. C. Davis, J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. A 1, 612–619 (1984).
    [CrossRef]
  8. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1987).
  9. X. Yan, R. M. Leahy, “Derivation and analysis of a filtered backprojection algorithm for cone-beam projection data,” IEEE Trans. Med. Imaging 10, 462–472 (1991).
    [CrossRef]
  10. J. Hsieh, Computed Tomography Principle, Design, Artifacts, Recent Advances, Vol. PM114 of the SPIE Press Monographs (SPIE, 2003).
  11. L. D. Loo, “CT Acceptance testing,” in Specification, Acceptance Testing and Quality Control of Diagnostic X-ray Imaging Equipment, J. A. Seibert, G. T. Barnes, R. G. Gould, eds. (American Association of Physicists in Medicine, 1994).
  12. S. M. Bentzen, “Evaluation of the spatial resolution of a CT scanner by direct analysis of the edge response function,” Med. Phys. 10, 579–581 (1983).
    [CrossRef] [PubMed]
  13. K. Mueller, R. Yagel, J. J. Wheller, “Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods,” IEEE Trans. Med. Imaging 18, 519–537 (1999).
    [CrossRef] [PubMed]
  14. J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
    [CrossRef] [PubMed]
  15. Z. Chen, R. Ning, “Pitfalls in cone-beam CT point-spread-function measurement by micro phantom reconstruction,” Opt. Eng. 44, 017002-1-8 (2005).
    [CrossRef]
  16. I. A. Cunningham, A. Fenster, “A method for modulation transfer function determination from edge profiles with correction for finite element differentiation,” Med. Phys. 14, 533–537 (1987).
    [CrossRef] [PubMed]
  17. J. M. Boone, J. A. Seibert, “An analytic edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21, 1541–1545 (1994).
    [CrossRef] [PubMed]
  18. Z. Chen, R. Ning, “Filling the Radon domain of computed tomography by local convex combination,” Appl. Opt. 42, 7043–7051 (2003).
    [CrossRef] [PubMed]
  19. H. Turbell, “Cone-beam reconstruction using filtered backprojection,” Ph.D. dissertation (Linkopings University, 2001).
  20. Z. Chen, T. Xu, S. Molloi, “Vessel diameter estimation in X-ray image using a watergauge algorithm,” J. Electron. Imaging 12, 724–742 (2003).
    [CrossRef]
  21. J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
    [CrossRef]
  22. Z. Chen, R. Ning, “Breast volume denoising and noise characterization by 3D wavelet transform,” Comput. Med. Imaging Graph. 28, 235–246 (2004).
    [CrossRef] [PubMed]

2005 (2)

Z. Chen, R. Ning, “Pixel-pyramid model for divergent projection geometry,” Opt. Eng. 44, 027002-1-10 (2005).
[CrossRef]

Z. Chen, R. Ning, “Pitfalls in cone-beam CT point-spread-function measurement by micro phantom reconstruction,” Opt. Eng. 44, 017002-1-8 (2005).
[CrossRef]

2004 (2)

Z. Chen, R. Ning, “Breast volume denoising and noise characterization by 3D wavelet transform,” Comput. Med. Imaging Graph. 28, 235–246 (2004).
[CrossRef] [PubMed]

Z. Chen, R. Ning, “Three-dimensional PSF measurement of cone-beam CT system by iterative edge-blurring algorithm,” Phys. Med. Biol. 49, 1865–1880 (2004).
[CrossRef] [PubMed]

2003 (4)

R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
[CrossRef] [PubMed]

Z. Chen, R. Ning, “Filling the Radon domain of computed tomography by local convex combination,” Appl. Opt. 42, 7043–7051 (2003).
[CrossRef] [PubMed]

Z. Chen, T. Xu, S. Molloi, “Vessel diameter estimation in X-ray image using a watergauge algorithm,” J. Electron. Imaging 12, 724–742 (2003).
[CrossRef]

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

2000 (1)

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

1999 (1)

K. Mueller, R. Yagel, J. J. Wheller, “Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods,” IEEE Trans. Med. Imaging 18, 519–537 (1999).
[CrossRef] [PubMed]

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

1994 (1)

J. M. Boone, J. A. Seibert, “An analytic edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21, 1541–1545 (1994).
[CrossRef] [PubMed]

1991 (1)

X. Yan, R. M. Leahy, “Derivation and analysis of a filtered backprojection algorithm for cone-beam projection data,” IEEE Trans. Med. Imaging 10, 462–472 (1991).
[CrossRef]

1987 (1)

I. A. Cunningham, A. Fenster, “A method for modulation transfer function determination from edge profiles with correction for finite element differentiation,” Med. Phys. 14, 533–537 (1987).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

S. M. Bentzen, “Evaluation of the spatial resolution of a CT scanner by direct analysis of the edge response function,” Med. Phys. 10, 579–581 (1983).
[CrossRef] [PubMed]

Bentzen, S. M.

S. M. Bentzen, “Evaluation of the spatial resolution of a CT scanner by direct analysis of the edge response function,” Med. Phys. 10, 579–581 (1983).
[CrossRef] [PubMed]

Boone, J. M.

J. M. Boone, J. A. Seibert, “An analytic edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21, 1541–1545 (1994).
[CrossRef] [PubMed]

Chen, B.

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

Chen, Z.

Z. Chen, R. Ning, “Pixel-pyramid model for divergent projection geometry,” Opt. Eng. 44, 027002-1-10 (2005).
[CrossRef]

Z. Chen, R. Ning, “Pitfalls in cone-beam CT point-spread-function measurement by micro phantom reconstruction,” Opt. Eng. 44, 017002-1-8 (2005).
[CrossRef]

Z. Chen, R. Ning, “Breast volume denoising and noise characterization by 3D wavelet transform,” Comput. Med. Imaging Graph. 28, 235–246 (2004).
[CrossRef] [PubMed]

Z. Chen, R. Ning, “Three-dimensional PSF measurement of cone-beam CT system by iterative edge-blurring algorithm,” Phys. Med. Biol. 49, 1865–1880 (2004).
[CrossRef] [PubMed]

Z. Chen, R. Ning, “Filling the Radon domain of computed tomography by local convex combination,” Appl. Opt. 42, 7043–7051 (2003).
[CrossRef] [PubMed]

Z. Chen, T. Xu, S. Molloi, “Vessel diameter estimation in X-ray image using a watergauge algorithm,” J. Electron. Imaging 12, 724–742 (2003).
[CrossRef]

Z. Chen, R. Ning, D. Conover, “Accurate perspective projection calculation using a pixel-pyramid model for iterative cone-beam reconstruction,” in Physics of Medical Imaging, M. Yaffe, L. Antonuk, eds., Proc. SPIE5030, 728–739 (2003).

Conover, D.

R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
[CrossRef] [PubMed]

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

Z. Chen, R. Ning, D. Conover, “Accurate perspective projection calculation using a pixel-pyramid model for iterative cone-beam reconstruction,” in Physics of Medical Imaging, M. Yaffe, L. Antonuk, eds., Proc. SPIE5030, 728–739 (2003).

Cunningham, I. A.

I. A. Cunningham, A. Fenster, “A method for modulation transfer function determination from edge profiles with correction for finite element differentiation,” Med. Phys. 14, 533–537 (1987).
[CrossRef] [PubMed]

Davis, L. C.

Feldkamp, L. A.

Fenster, A.

I. A. Cunningham, A. Fenster, “A method for modulation transfer function determination from edge profiles with correction for finite element differentiation,” Med. Phys. 14, 533–537 (1987).
[CrossRef] [PubMed]

Frei, T.

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Hoffman, E.

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Hsieh, J.

J. Hsieh, Computed Tomography Principle, Design, Artifacts, Recent Advances, Vol. PM114 of the SPIE Press Monographs (SPIE, 2003).

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

Jiang, M.

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1987).

Kress, J. W.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Leahy, R. M.

X. Yan, R. M. Leahy, “Derivation and analysis of a filtered backprojection algorithm for cone-beam projection data,” IEEE Trans. Med. Imaging 10, 462–472 (1991).
[CrossRef]

Loo, L. D.

L. D. Loo, “CT Acceptance testing,” in Specification, Acceptance Testing and Quality Control of Diagnostic X-ray Imaging Equipment, J. A. Seibert, G. T. Barnes, R. G. Gould, eds. (American Association of Physicists in Medicine, 1994).

Meinel, J. F.

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Molloi, S.

Z. Chen, T. Xu, S. Molloi, “Vessel diameter estimation in X-ray image using a watergauge algorithm,” J. Electron. Imaging 12, 724–742 (2003).
[CrossRef]

Mueller, K.

K. Mueller, R. Yagel, J. J. Wheller, “Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods,” IEEE Trans. Med. Imaging 18, 519–537 (1999).
[CrossRef] [PubMed]

Ning, R.

Z. Chen, R. Ning, “Pixel-pyramid model for divergent projection geometry,” Opt. Eng. 44, 027002-1-10 (2005).
[CrossRef]

Z. Chen, R. Ning, “Pitfalls in cone-beam CT point-spread-function measurement by micro phantom reconstruction,” Opt. Eng. 44, 017002-1-8 (2005).
[CrossRef]

Z. Chen, R. Ning, “Breast volume denoising and noise characterization by 3D wavelet transform,” Comput. Med. Imaging Graph. 28, 235–246 (2004).
[CrossRef] [PubMed]

Z. Chen, R. Ning, “Three-dimensional PSF measurement of cone-beam CT system by iterative edge-blurring algorithm,” Phys. Med. Biol. 49, 1865–1880 (2004).
[CrossRef] [PubMed]

R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
[CrossRef] [PubMed]

Z. Chen, R. Ning, “Filling the Radon domain of computed tomography by local convex combination,” Appl. Opt. 42, 7043–7051 (2003).
[CrossRef] [PubMed]

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

Z. Chen, R. Ning, D. Conover, “Accurate perspective projection calculation using a pixel-pyramid model for iterative cone-beam reconstruction,” in Physics of Medical Imaging, M. Yaffe, L. Antonuk, eds., Proc. SPIE5030, 728–739 (2003).

Ning, Y.

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Seibert, J. A.

J. M. Boone, J. A. Seibert, “An analytic edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21, 1541–1545 (1994).
[CrossRef] [PubMed]

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1987).

Tang, X.

R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
[CrossRef] [PubMed]

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

Turbell, H.

H. Turbell, “Cone-beam reconstruction using filtered backprojection,” Ph.D. dissertation (Linkopings University, 2001).

Vannier, M.

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Wang, G.

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Wheller, J. J.

K. Mueller, R. Yagel, J. J. Wheller, “Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods,” IEEE Trans. Med. Imaging 18, 519–537 (1999).
[CrossRef] [PubMed]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Xu, T.

Z. Chen, T. Xu, S. Molloi, “Vessel diameter estimation in X-ray image using a watergauge algorithm,” J. Electron. Imaging 12, 724–742 (2003).
[CrossRef]

Yagel, R.

K. Mueller, R. Yagel, J. J. Wheller, “Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods,” IEEE Trans. Med. Imaging 18, 519–537 (1999).
[CrossRef] [PubMed]

Yan, X.

X. Yan, R. M. Leahy, “Derivation and analysis of a filtered backprojection algorithm for cone-beam projection data,” IEEE Trans. Med. Imaging 10, 462–472 (1991).
[CrossRef]

Yu, R.

R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
[CrossRef] [PubMed]

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

Acad. Radiol. (1)

J. F. Meinel, G. Wang, M. Jiang, T. Frei, M. Vannier, E. Hoffman, “Spatial variation of resolution and noise in multidetector row spiral CT,” Acad. Radiol. 10, 607–613 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

Comput. Med. Imaging Graph. (1)

Z. Chen, R. Ning, “Breast volume denoising and noise characterization by 3D wavelet transform,” Comput. Med. Imaging Graph. 28, 235–246 (2004).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (3)

K. Mueller, R. Yagel, J. J. Wheller, “Anti-aliased three-dimensional cone-beam reconstruction of low-contrast objects with algebraic methods,” IEEE Trans. Med. Imaging 18, 519–537 (1999).
[CrossRef] [PubMed]

R. Ning, B. Chen, R. Yu, D. Conover, X. Tang, Y. Ning, “Flat panel detector-based cone-beam volume CT angiography imaging: system evaluation,” IEEE Trans. Med. Imaging 19, 949–963 (2000).
[CrossRef] [PubMed]

X. Yan, R. M. Leahy, “Derivation and analysis of a filtered backprojection algorithm for cone-beam projection data,” IEEE Trans. Med. Imaging 10, 462–472 (1991).
[CrossRef]

J. Electron. Imaging (1)

Z. Chen, T. Xu, S. Molloi, “Vessel diameter estimation in X-ray image using a watergauge algorithm,” J. Electron. Imaging 12, 724–742 (2003).
[CrossRef]

J. Opt. Soc. Am. A (1)

Med. Phys. (4)

I. A. Cunningham, A. Fenster, “A method for modulation transfer function determination from edge profiles with correction for finite element differentiation,” Med. Phys. 14, 533–537 (1987).
[CrossRef] [PubMed]

J. M. Boone, J. A. Seibert, “An analytic edge spread function model for computer fitting and subsequent calculation of the LSF and MTF,” Med. Phys. 21, 1541–1545 (1994).
[CrossRef] [PubMed]

R. Ning, X. Tang, D. Conover, R. Yu, “Flat panel detector-based cone beam computed tomography with a circle-plus-two arcs data acquisition orbit: preliminary phantom study,” Med. Phys. 30, 1694–1705 (2003).
[CrossRef] [PubMed]

S. M. Bentzen, “Evaluation of the spatial resolution of a CT scanner by direct analysis of the edge response function,” Med. Phys. 10, 579–581 (1983).
[CrossRef] [PubMed]

Opt. Eng. (2)

Z. Chen, R. Ning, “Pitfalls in cone-beam CT point-spread-function measurement by micro phantom reconstruction,” Opt. Eng. 44, 017002-1-8 (2005).
[CrossRef]

Z. Chen, R. Ning, “Pixel-pyramid model for divergent projection geometry,” Opt. Eng. 44, 027002-1-10 (2005).
[CrossRef]

Phys. Med. Biol. (1)

Z. Chen, R. Ning, “Three-dimensional PSF measurement of cone-beam CT system by iterative edge-blurring algorithm,” Phys. Med. Biol. 49, 1865–1880 (2004).
[CrossRef] [PubMed]

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Other (6)

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

Z. Chen, R. Ning, D. Conover, “Accurate perspective projection calculation using a pixel-pyramid model for iterative cone-beam reconstruction,” in Physics of Medical Imaging, M. Yaffe, L. Antonuk, eds., Proc. SPIE5030, 728–739 (2003).

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1987).

J. Hsieh, Computed Tomography Principle, Design, Artifacts, Recent Advances, Vol. PM114 of the SPIE Press Monographs (SPIE, 2003).

L. D. Loo, “CT Acceptance testing,” in Specification, Acceptance Testing and Quality Control of Diagnostic X-ray Imaging Equipment, J. A. Seibert, G. T. Barnes, R. G. Gould, eds. (American Association of Physicists in Medicine, 1994).

H. Turbell, “Cone-beam reconstruction using filtered backprojection,” Ph.D. dissertation (Linkopings University, 2001).

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Figures (8)

Fig. 1
Fig. 1

(a) Object domain of cone-beam tomography; (b) spatial samplings of detector and object domain.

Fig. 2
Fig. 2

Volumetric reconstruction by voxel-driven backprojection. (a) A voxel-driven ray that originates from the x-ray source passes through the voxel center and reaches the detector; (b) voxel subdivision and multiple voxel-driven rays; (c1) bilinear interpolation; (c2) inverse-distance-weighted interpolation.

Fig. 3
Fig. 3

Demonstration of a multigrid image representation by multigrid sampling. A Gaussian spot is digitally represented by arrays of (a) 11 × 11, (b) 21 × 21, and (c) 41 × 41. The profiles corresponding to the scan lines in (a)–(c) are plotted in (a1)–(c1), respectively. The available entries are marked by *.

Fig. 4
Fig. 4

Demonstration of multigrid image representation by image interpolation. Images (a) and (b) are generated from Fig. 3(a) by linear interpolations with upsampling factors 2 and 4, respectively. The available entries are marked by *.

Fig. 5
Fig. 5

(a) Cross-sectional image (central x-slice image of 61 × 61 array) of a reconstructed digital Teflon ball from our cone-beam tomography prototype. The Teflon ball (diameter ~5 mm) was located at (0, 0, 6 cm) in the object domain during the cone-beam scan. The volume was reconstructed in the proper CT grid (voxel size of 0.1843 mm). The profile of the scan line on the digital image is plotted in (b), where the available entries are marked by *.

Fig. 6
Fig. 6

Slice images of a Teflon ball (the same as used in Fig. 5) under supergridded cone-beam reconstruction: (a1) 121 × 121 and (b1) 241 × 241. Meanwhile, (a2) 121 × 121 and (b2) 241 × 241 show the grid-refined images from Fig. 5(a) by image interpolation. The horizontal scan lines were added to extract the profiles, as shown in Fig. 7.

Fig. 7
Fig. 7

Demonstration of scan-line profiles under two grid resolutions and two grid refinement techniques. The two profiles at the low-grid resolution in (a) are extracted from Figs. 6(a1) and 6(a2), and the two profiles at the high-grid resolution in (b) are from Figs. 6(b1) and 6(b2).

Fig. 8
Fig. 8

(a) Illustration of radial scan lines for edge profile extraction; (b) the edge profiles of radial scan lines. (In our experiment, more radial scan lines were used).

Tables (1)

Tables Icon

Table 1 PSF Calculations with Multigrid Images Generated by Supergridded Reconstruction and Postreconstruction Processing

Equations (18)

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

g ( α , θ ) = 0 f [ Φ ( θ ) + t α ] d t ,
Ω 0 = { ( x , y , z ) [ - x max / 2 , x max / 2 ] [ - y max / 2 , y max / 2 ] [ - z max / 2 , z max / 2 ] } .
g ˜ ( z 1 , z 2 , θ ) = lim ɛ 0 - D z 1 2 + z 2 2 + D 2 × g ( z 1 , z 2 , θ ) E ɛ ( z 1 - z 1 ) d z 1 ,
f ^ ( x , y , z ) = R D 4 π 2 0 2 π g ˜ ( z 1 , z 2 , θ ) ( x cos θ + y sin θ - R ) 2 × d θ , ( x , y , z ) Ω 0 ,
E ɛ ( α ^ 1 ) = { 1 / ɛ 2 , α ^ 1 < ɛ - 1 / α ^ 1 2 , α ^ 1 ɛ ,
Ω Ω 0 .
f [ m , n , k ] = 1 δ x δ y δ z f ( x , y , z ) * * * rect × ( x - m δ x δ x , y - n δ y δ y , z - k δ z δ z ) ,
δ x = x max / M , δ y = y max / N , δ z = z max / K ,
f ^ [ m , n , k ] = R D 4 π 2 0 2 π g ˜ ( z 1 , z 2 , θ ) ( m δ x cos θ + n δ y sin θ - R ) 2 × d θ , [ m , n , k ] [ Ω 0 ] .
x = m δ x , m [ 1 , M ] , y = n δ y , n [ 1 , N ] , z = k δ z , k [ 1 , K ] .
δ 0 = Δ 0 R / D ,
δ < δ 0 .
δ = δ 0 / 2 j ,             j = 1 , 2 , 3 , .
s ( t ) = s 0 ( t ) * h ( t ) + n ( t ) ,
h σ ( t ) = 1 2 π σ exp ( - t 2 2 σ 2 ) .
fit error = min s ( t ) - s 0 ( t ) * h σ ( t ) .
σ opt = arg min σ s ( t ) - s 0 ( t ) * h σ ( t ) .
FWHM = 2.3546 δ σ opt .

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