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INSTITUTE OF PHYSICS PUBLISHING INVERSE PROBLEMS Inverse Problems 21 (2005) 473485 doi:10.1088/0266-5611/21/2/004
 

Summary: INSTITUTE OF PHYSICS PUBLISHING INVERSE PROBLEMS
Inverse Problems 21 (2005) 473485 doi:10.1088/0266-5611/21/2/004
On the injectivity of the circular Radon transform
Gaik Ambartsoumian and Peter Kuchment
Mathematics Department, Texas A & M University, College Station, TX 77843-3368, USA
E-mail: kuchment@math.tamu.edu and haik@tamu.edu
Received 13 July 2004, in final form 14 January 2005
Published 1 February 2005
Online at stacks.iop.org/IP/21/473
Abstract
The circular Radon transform integrates a function over the set of all spheres
with a given set of centres. The problem of injectivity of this transform (as
well as inversion formulae, range descriptions, etc) arises in many fields from
approximation theory to integral geometry, to inverse problems for PDEs and
recently to newly developing types of tomography. A major breakthrough in
the 2D case was made several years ago in a work by Agranovsky and Quinto.
Their techniques involved microlocal analysis and known geometric properties
of zeros of harmonic polynomials in the plane. Since then there has been an
active search for alternative methods, especially those based on simple PDE
techniques, which would be less restrictive in more general situations. This

  

Source: Ambartsoumian, Gaik - Department of Mathematics, University of Texas at Arlington

 

Collections: Mathematics