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Reconstruction from X-Rays

  • K. T. Smith
  • S. L. Wagner
  • R. B. Guenther
  • D. C. Solmon
Part of the The IBM Research Symposia Series book series (IRSS)

Abstract

According to T.J. Rivlin (these Proc.) “The problem of optimal recovery is that of approximating as effectively as possible a given map of any function known to belong to a certain class from limited and possibly error-contaminated information about it.” More precisely, in the scheme envisioned by Rivlin there are given spaces X of possible objects, Y of possible data, and Z of possible reconstructions of certain features of the objects.

Keywords

Density Function Reconstruction Method Inversion Formula Finite Dimensional Space Optimal Recovery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. Guenther, C. Kerber, E. Killian, K. Smith, and S. Wagner, “Reconstruction of Objects from Radiographs and the Location of Brain Tumors”, Proc. Natl. Acad. Sci. USA 71: 4884–4886 (1974).CrossRefGoogle Scholar
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    R. Mersereau and A. Oppenheim, “Digital Reconstruction of Multidimensional Signals from their Projections”, Proc. IEEE 62: 1319–1338 (1974).CrossRefGoogle Scholar
  3. 3.
    K. Smith, D. Solmon, and S. Wagner, “Practical and Mathematical Aspects of the Problem of Reconstructing Objects from Radiographs”, Bull. Amer. Math. Soc. (To appear).Google Scholar
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    K. Smith, S. Wagner, R. Guenther, and D. Solmon, “The Diagnosis of Breast Cancer in Mammograms by the Evaluation of Density Patterns” (To appear).Google Scholar
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    K. Smith, S. Wagner, R. Guenther, and D. Solmon, “Computerized Axial Tomography from Ordinary Radiographs - An Alternative to Scanners” (To appear).Google Scholar
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    D. Solmon, K. Smith, S. Wagner, and R. Guenther, “Breast Cancer Diagnosis from Density Studies of Mamograms”, International Conference on Cybernetics and Society, IEEE, November 1–3, 1976, Washington, D. C.Google Scholar
  7. 7.
    D. Solmon and C. Hamaker, “The Rate of Convergence of the Kacmarz Method”, J. Math. Anal. & Appl. (To appear).Google Scholar
  8. 8.
    S. Wagner, K. Smith, R. Guenther, and D. Solmon, “Computer Assisted Densitometric Detection of Breast Cancer”, Application of Optical Instrumentation in Medicine V, SPIE 96: 418–422 (1976).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • K. T. Smith
    • 1
  • S. L. Wagner
    • 1
  • R. B. Guenther
    • 1
  • D. C. Solmon
    • 2
  1. 1.Oregon State UniversityCorvallisUSA
  2. 2.State University of New York at BuffaloNew YorkUSA

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