Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1637-1646.doi: 10.1016/S0252-9602(12)60130-1

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NON-UNIQUENESS OF THE RECONSTRUCTION FOR CONNECTED AND SIMPLY CONNECTED SETS IN THE PLANE BY THEIR FIXED#br# FINITE PROJECTIONS

Takashi Takiguchi   

  1. Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan
  • Received:2009-02-12 Revised:2011-03-07 Online:2012-07-20 Published:2012-07-20

Abstract:

We discuss a problem to reconstruct the measurable sets in the plane from their fixed finite projections. In the main theorem, we construct an example of connected and simply connected polygons which are not uniquely reconstructed by their fixed finite projections. We also make a comparison between our main theorem and the known results on this problem.

Key words: Radon transform, inverse problem

CLC Number: 

  • 44A12
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