Integral Geometry and Tomography

  • Victor Isakov
Part of the Applied Mathematical Sciences book series (AMS, volume 127)


The problems of integral geometry are to determine a function given (weighted) integrals of this function over a “rich” family of manifolds. These problems are of importance in medical applications (tomography), and they are quite useful for dealing with inverse problems in hyperbolic differential equations (integrals of unknown coefficients over ellipsoids or lines can be obtained from the first terms of the asymptotic expansion of rapidly oscillating solutions and information about first arrival times of a wave). While there has been significant progress in the classical Radon problem when manifolds are hyperplanes and the weight function is unity, the situation is not quite clear even when the weight function is monotone along, say, straight lines in the plane case (attenuation). We give a brief review of this area, referring for more information to the book of Natterer [Nat].


Weight Function Attenuation Coefficient Pseudodifferential Operator Integral Geometry Constant Attenuation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Victor Isakov
    • 1
  1. 1.Department of Mathematics and StatisticsThe Wichita State UniversityWichitaUSA

Personalised recommendations