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The Method of Moments in Tomography and Quantum Mechanics

In: Distributions with given Marginals and Moment Problems

Author

Listed:
  • L. B. Klebanov

    (St. Petersburg State University for Architecture and Civil Engineering)

  • S. T. Rachev

    (University of California Santa Barbara)

Abstract

Suppose an x-ray examination of an object (a body) is performed, and the intensities of the x-ray at both input (I i) and output (I o) are measured. It is known, that (under some conditions imposed on the object and the intensity of the input x-ray) the following is true: $$log(\frac{I_i}{I_o})=\int _L p(x)dL$$ , where the integral is taken along L, the straight line which the x-ray follows through the body. The problem is to reconstruct the density p of the body based on the line integrals calculated on (some or all) of the straight lines.

Suggested Citation

  • L. B. Klebanov & S. T. Rachev, 1997. "The Method of Moments in Tomography and Quantum Mechanics," Springer Books, in: Viktor Beneš & Josef Štěpán (ed.), Distributions with given Marginals and Moment Problems, pages 35-52, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5532-8_5
    DOI: 10.1007/978-94-011-5532-8_5
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