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Algebraic Reconstruction of Spatial Distributions of Acoustic Absorption within Tissue from Their Two-Dimensional Acoustic Projections

  • J. F. Greenleaf
  • S. A. Johnson
  • S. L. Lee
  • G. T. Hermant
  • E. H. Woo

Abstract

It has been known for many years that three-dimensional information concerning the spatial distribution of energy absorbers within an object could be obtained from two-dimensional shadow projections of the energy absorption of the object (1). Two-dimensional projections or shadows of the absorption of an object can be obtained using many forms of energy such as light, x-radiation, electrons, or sound. The problem was treated in abstract mathematics as early as 1917 by Radon (2). The first practical solution of this problem was obtained by Bracewell in 1954 (3) who applied the technique to radioastronomy. The first application of these kinds of techniques to biology were probably done by DeRosier and Klug who obtained the cross-sectional structure of the tail of a bacteria phage from one-dimensional projections obtained with electrons in an electron microscope (4).

Keywords

Ultrasonic Energy Canine Heart Energy Absorber Algebraic Reconstruction Technique Acoustic Absorption 
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.
    Gordon, R., G. T. Herman (1971): Reconstruction of pictures from their projections. Comm ACM 14(12): 759–768.MATHCrossRefGoogle Scholar
  2. 2.
    Radon, J. (1917): Ueber die Bestimmung von Functionen durch ihre integralwerte Laengs gewisser Manningfoltigkeiten (on the determination of functions from their integrals along certain manifolds) Berichte Saechsische Acadamie der Wissenschaften (Leipzig) Mathematische-Physische Klasse 69, 262–277.Google Scholar
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    Bracewell, R. N., and J. A. Roberts (1954): Aerial smoothing in radio astronomy. Aust J Phys 7(4): 615–640.ADSCrossRefGoogle Scholar
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    DeRosier, D. J., and A. Klug (1968): Reconstructions of three-dimensional structures from electron micrographs. Nature 217: 130–134.ADSCrossRefGoogle Scholar
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    Robb, R. A., S. A. Johnson, J. F. Greenleaf, M. A. Wondrow, and E. H. Wood: An operator-interactive computer-controlled system for high fidelity digitization and analysis of biomedical images. SPIE Proc Quantitative Imagery in Biomed Sci II, San Diego, August 1973 (in press).Google Scholar

Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • J. F. Greenleaf
    • 1
  • S. A. Johnson
    • 1
  • S. L. Lee
    • 1
  • G. T. Hermant
    • 2
  • E. H. Woo
    • 1
  1. 1.Department of PhysiologyMayo FoundationRochesterUSA
  2. 2.SUNYBuffaloUSA

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