OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 73, Iss. 11 — Nov. 1, 1983
  • pp: 1493–1500

Iterative convolution backprojection algorithms for image reconstruction from limited data

Barry P. Medoff, William R. Brody, Menahem Nassi, and Albert Macovski  »View Author Affiliations


JOSA, Vol. 73, Issue 11, pp. 1493-1500 (1983)
http://dx.doi.org/10.1364/JOSA.73.001493


View Full Text Article

Enhanced HTML    Acrobat PDF (3382 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Image-reconstruction algorithms implemented on existing computerized tomography (CT) scanners require the collection of line integrals that are evenly spaced over 360 deg. In many practical situations, some of the line integrals are inaccurately measured or are not measured at all. In these limited-data situations, conventional algorithms produce images with severe streak artifacts. Recently, several other image-reconstruction algorithms were suggested, each tailored to a specific type of limited-data problem. These algorithms make minimal use of a priori knowledge about the image; only one has been demonstrated with real x-ray data. We present a new operator framework that treats all types of limited-data image-reconstruction problems in a unified way. From this framework we derive iterative convolution backprojection algorithms that make no restrictions on the location of missing line integrals. All available a priori information is incorporated by constraint operators. The algorithm has been implemented on a commercial CT scanner. We present examples of images reconstructed from real x-ray data in two limited-data situations and demonstrate the use of additional a priori information to reduce streak artifacts further.

© 1983 Optical Society of America

Citation
Barry P. Medoff, William R. Brody, Menahem Nassi, and Albert Macovski, "Iterative convolution backprojection algorithms for image reconstruction from limited data," J. Opt. Soc. Am. 73, 1493-1500 (1983)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-73-11-1493


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. S. Harell, D. F. Guthaner, R. S. Breiman, C. C. Morehouse, E. J. Seppi, W. H. Marshall, and L. Wexler, "Stop-action cardiac computed tomography," Radiology 123, 515–517 (1977). [PubMed]
  2. G. H. Glover and N. J. Peic, "An algorithm for the reduction of metal clip artifacts in CT reconstructions," Med. Phys. 8,799–807 (1981). [CrossRef] [PubMed]
  3. R. M. Lewitt and R. H. T. Bates, "Image reconstruction from projections: III: Projection completion methods (theory)," Optik 50, 189–204 (1978).
  4. R. M. Lewitt and R. H. T. Bates, "Image reconstruction from projections: IV: Projection completion methods (computational examples)," Optik 50, 269–278 (1978).
  5. A. Peres, "Tomographic reconstruction from limited angular data," J. Comput. Assisted Tomog. 3, 800–803 (1979).
  6. T. Inouye, "Image reconstruction with limited angle projection data," IEEE Trans. Nucl. Sci. NS-26, 2666–2669 (1979).
  7. T. Inouye, "Image reconstruction with limited view angle projections," in Proceedings of the International Workshop on Physics and Engineering in Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 165–168. [CrossRef]
  8. R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709–720 (1974). [CrossRef]
  9. A. Papoulis, "A new algorithm in spectral analysis and bandlimited extrapolation," IEEE Trans. Circuits Syst. CAS-22, 735–742 (1975). [CrossRef]
  10. T. Sato, S. J. Norton, M. Linzer, O. Ikeda, and M. Hirama, "Tomographic image reconstruction from limited projections using iterative revisions in image and transform spaces," Appl. Opt. 20, 395–399 (1981). [CrossRef] [PubMed]
  11. K. C. Tam and V. Perez-Mendez, "Tomographical imaging with limited-angle input," J. Opt. Soc. Am. 71, 582–592 (1981). [CrossRef]
  12. K. C. Tam and V. Perez-Mendez, "Limited-angle three dimensional reconstructions using Fourier transform iterations and Radon transform iterations," Opt. Engin. 20, 586–589 (1981). [CrossRef]
  13. B. K. P. Horn, "Fan-beam reconstruction methods," Proc. IEEE 67, 1616–1623 (1979). [CrossRef]
  14. A. Lent and H. Tuy, "An iterative method for the extrapolation of band-limited functions," J. Math. Anal. Appl. 83, 554–565 (1981). [CrossRef]
  15. D. C. Youla and H. Webb, "Image restoration by the method of convex projections: Part 1—Theory," IEEE Trans. Med. Imaging MI-1, 81–94 (1982). [CrossRef]
  16. M. I. Sezan and H. Stark, "Image restoration by the method of convex projections: Part 2—Applications and numerical results," IEEE Trans. Med. Imaging MI-1, 95–101 (1982). [CrossRef]
  17. M. Nassi, W. R. Brody, B. P. Medoff, and A. Macovski, "Iterative reconstruction—reprojection: an algorithm for limited data cardiac computed tomography," IEEE Trans. Biomed. Eng. BME-29, 333–341 (1982). [CrossRef]
  18. M. Ein-Gal, D. Rosenfeld, and A. Macovski, "The consistency of the shadow: an approach to preprocessing in computerized tomography," in Digest of Topical Meeting on Image Processing for 2-D and 3-D Reconstruction from Projections (Optical Society of America, Washington, D.C., 1975), paper WB5.
  19. A. K. Louis, "Ghosts in tomography—the null space of the radon transform," Math. Meth. Appl. Sci. 3, 1–10 (1981). [CrossRef]
  20. D. G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1969).
  21. B. P. Medoff, W. R. Brody, and A. Macovski, "Image reconstruction from limited data," in Proceedings of the International Workshop on Physics and Engineering in Medical Imaging(Institute of Electrical and Electronics Engineers, New York, 1982), pp. 188–192. [CrossRef]
  22. M. Ein-Gal, "The shadow transform—an approach to cross sectional imaging," Ph.D. Thesis (Stanford University, Stanford, Calif., 1974).
  23. S. L. Wood, A. Macovski, and M. Morf, "Reconstructions with limited data using estimation theory," in Computer Aided Tomography and Ultrasonics in Medicine, J. Raviv et al., eds. (North-Holland, Amsterdam, 1979), pp. 219–233.
  24. M. H. Buonocore, "Fast minimum variance estimators for limited angle computed tomography image reconstruction," Ph.D. Thesis (Stanford University, Stanford, Calif., 1981).
  25. K. M. Hanson, "Limited angle CT reconstruction using a priori information," in Proceedings of the IEEE Computer Society International Symposium (Institute of Electrical and Electronics Engineers, New York, 1982).
  26. R. W. Schafer, R. M. Mersereau, M. A. Richards, "Constrained iterative restoration algorithms," Proc. IEEE 69, 432–450 (1981). [CrossRef]
  27. B. P. Medoff, "Image reconstruction from limited data," Ph.D. Thesis (Stanford University, Stanford, Calif., 1983).

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  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited