OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 24 — Nov. 22, 2010
  • pp: 25306–25320

SVD for imaging systems with discrete rotational symmetry

Eric Clarkson, Robin Palit, and Matthew A. Kupinski  »View Author Affiliations


Optics Express, Vol. 18, Issue 24, pp. 25306-25320 (2010)
http://dx.doi.org/10.1364/OE.18.025306


View Full Text Article

Acrobat PDF (2189 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The singular value decomposition (SVD) of an imaging system is a computationally intensive calculation for tomographic imaging systems due to the large dimensionality of the system matrix. The computation often involves memory and storage requirements beyond those available to most end users. We have developed a method that reduces the dimension of the SVD problem towards the goal of making the calculation tractable for a standard desktop computer. In the presence of discrete rotational symmetry we show that the dimension of the SVD computation can be reduced by a factor equal to the number of collection angles for the tomographic system. In this paper we present the mathematical theory for our method, validate that our method produces the same results as standard SVD analysis, and finally apply our technique to the sensitivity matrix for a clinical CT system. The ability to compute the full singular value spectra and singular vectors will augment future work in system characterization, image-quality assessment and reconstruction techniques for tomographic imaging systems.

© 2010 Optical Society of America

OCIS Codes
(110.2960) Imaging systems : Image analysis
(110.3000) Imaging systems : Image quality assessment
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
Imaging Systems

History
Original Manuscript: August 13, 2010
Revised Manuscript: November 11, 2010
Manuscript Accepted: November 11, 2010
Published: November 19, 2010

Citation
Eric Clarkson, Robin Palit, and Matthew A. Kupinski, "SVD for imaging systems with discrete rotational symmetry," Opt. Express 18, 25306-25320 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-24-25306


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. H. H. Barrett, J. N. Aarsvold, and T. J. Roney, "Null functions and eigenfunctions: tools for the analysis of imaging systems," Prog. Clin. Biol. Res. 363, 211-226 (1991).
  2. H. Barrett, and K. Myers, Foundations of Image Science (John Wiley and Sons, 2004).
  3. A. K. Jorgensen, and G. L. Zeng, "SVD-based evaluation of multiplexing in multipinhole SPECT systems," Int. J. Biomed. Imaging 2008, 769195 (2008).
  4. Y. L. Hsieh, G. L. Zeng, and G. T. Gullberg, "Projection space image reconstruction using strip functions to calculate pixels more "natural" for modeling the geometric response of the SPECT collimator," IEEE Trans. Med. Imaging 17(1), 24-44 (1998). [CrossRef]
  5. G. Zeng, and G. Gullberg, "An SVD study of truncated transmission data in SPECT," IEEE Trans. Nucl. Sci. 44(1), 107-111 (1997). [CrossRef]
  6. G. Gullberg, and G. Zeng, "A reconstruction algorithm using singular value decomposition of a discrete representation of the exponential radon transform using natural pixels," IEEE Trans. Nucl. Sci. 41(6), 2812-2819 (1994). [CrossRef]
  7. S. Park, and E. Clarkson, "Efficient estimation of ideal-observer performance in classification tasks involving high-dimensional complex backgrounds," J. Opt. Soc. Am. A 26(11), 59-71 (2009). [CrossRef]
  8. S. Park, J. M. Witten, and K. J. Myers, "Singular vectors of a linear imaging system as efficient channels for the bayesian ideal observer," IEEE Trans. Med. Imaging 28(5), 657-668 (2009). [CrossRef]
  9. M. Hamermesh, Group Theory and its Application to Physical Problems (Dover Publications, 1989).
  10. E. Anderson, Z. Bai, and C. Bischof, LAPACK Users’ Guide (Society for Industrial Mathematics, 1999).
  11. J. Aarsvold, "Multiple-pinhole transaxial tomography: a model and analysis," Ph. D. Dissertation (University of Arizona, 1993).
  12. J. Aarsvold, and H. Barrett, "Symmetries of single-slice multiple-pinhole tomographs," in Conference Record of the 1996 IEEE NSS/MIC (IEEE, 1997), vol. 3, pp. 1673-1677.
  13. P. Varatharajah, B. Tankersley, and J. Aarsvold, "Discrete models and singular-value decompositions of single-slice imagers with orthogonal detectors," in Conference Record of the 1998 IEEE NSS/MIC (IEEE, 1999), vol. 2, pp. 1184-1188.
  14. S. Steckmann, M. Knaup, and M. Kachelrieß, "High performance cone-beam spiral backprojection with voxel-specific weighting," Phys. Med. Biol. 54(12), 3691-3708 (2009). [CrossRef]
  15. E. Isaacson, and H. Keller, Analysis of Numerical Methods (Dover Publications, 1994).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: MOV (40 KB)     
» Media 2: MOV (55 KB)     
» Media 3: MOV (57 KB)     
» Media 4: MOV (66 KB)     
» Media 5: MOV (53 KB)     
» Media 6: MOV (56 KB)     
» Media 7: MOV (71 KB)     
» Media 8: MOV (59 KB)     
» Media 9: MOV (70 KB)     
» Media 10: MOV (59 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited