Acta mathematica scientia,Series B ›› 2002, Vol. 22 ›› Issue (3): 311-318.

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A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R^N

 WANG Jin-Ping, DU Jin-Yuan   

  1. 1School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2Department of Mathematics, Hubei Normal University, Huangshi 435002, China
  • Online:2002-07-15 Published:2002-07-15
  • Supported by:

    Supported by the NNSF of China, RFDP of Higher Education

Abstract:

The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in Rn with respect to the weight W(x). It fulfilles mainly by means of the projection-slice theorem.The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately
leads to an inversion formula by series expansion and range characterizations.

Key words: Radon transform, projection-slice theorem, singular value decomposition

CLC Number: 

  • 44A15
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