OSA's Digital Library

Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 2, Iss. 6 — Mar. 16, 1998
  • pp: 254–260

Decomposition of images and objects into measurement and null components

D.W. Wilson and H.H. Barrett  »View Author Affiliations


Optics Express, Vol. 2, Issue 6, pp. 254-260 (1998)
http://dx.doi.org/10.1364/OE.2.000254


View Full Text Article

Enhanced HTML    Acrobat PDF (108 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We derive and discuss an algorithm for separating measurement-and null-space components of an object with respect to a given imaging system. This algorithm requires a discrete-to-discrete approximation of a typically continuous-to-discrete imaging system, and problems associated with such an approximation are examined. Situations where knowledge of the measurement and null spaces is crucial for analyzing imaging systems are discussed. We conclude with two examples demonstrating the usefulness of this algorithm, even in the discrete-to-discrete approximation.

© Optical Society of America

OCIS Codes
(100.6950) Image processing : Tomographic image processing
(110.6960) Imaging systems : Tomography

ToC Category:
Focus Issue: Tomographic image reconstruction

History
Original Manuscript: December 9, 1997
Published: March 16, 1998

Citation
Donald Wilson and Harrison Barrett, "Decomposition of images and objects into measurement and null components," Opt. Express 2, 254-260 (1998)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-6-254


Sort:  Journal  |  Reset  

References

  1. D.R. Gilland, B.M.W. Tsui, C.E. Metz and R.J. Jaszczak, J.R. Perry, "An evaluation of maximum likelihood-EM reconstruction for SPECT by ROC analysis," J. Nucl. Med. 33, 451-457 (1992). [PubMed]
  2. X-L. Xu, J S. Liow and S.C. Strother, "Iterative algebraic reconstruction algorithms for emission computed tomography: A unified framework and its application to positron emission tomography," Med. Phys., 20, 1675- 1684 (1993). [CrossRef] [PubMed]
  3. S.C. Moore, S.P. Kijewski, S.P. Muller and B.L. Holman, "SPECT Image Noise Power: Effects of Nonstationary Projection Noise and Attenuation Compensation," J. Nucl. Med. 29, 1704-1709, (1988). 4. H.H. Barrett, D.W. Wilson and B.M.W. Tsui, "Noise properties of the EM algorithm: I. Theory," Phys. Med. Biol. 39, 833-846 (1994). [PubMed]
  4. H.H. Barrett, D.W. Wilson and B.M.W. Tsui, "Noise properties of the EM algorithm: I. Theory," Phys. Med. Biol. 39, 833-846 (1994). [CrossRef] [PubMed]
  5. O.N. Strand, "Theory and methods related to the singular-function expansion and Landwebers iteration for integral equations of the first kind," SIAM J. Numer. Anal., 11, 798-825 (1974). [CrossRef]
  6. K.M. Hanson, "Bayesian and Related Methods in Image Reconstruction from Incomplete Data," in Image Recovery, Theory and Application, Henry Stark, ed. (Academic, Orlando, Fla. 1987)
  7. H.H. Barrett and D.W. Wilson, "An algorithm to calculate null and measurement spaces," http://www.radiology.arizona.edu/~fastspec/nul_spc.pdf
  8. P. Gilbert, "Iterative Methods for the Three-Dimensional Reconstruction of an Object from Projections," J. Theor. Biol. 36, 105-117 (1972). [CrossRef] [PubMed]
  9. H.H. Barrett, "The FASTSPECT imaging system," http://www.radiology.arizona.edu/~fastspec.
  10. I. Pang, "Wedge phantom for resolution measurement," http://www.radiology.arizona.edu/~fastspec/wedge.htm.

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.


« Previous Article

OSA is a member of CrossRef.

CrossCheck Deposited