数学物理学报(英文版) ›› 2002, Vol. 22 ›› Issue (3): 311-318.

• 论文 • 上一篇    下一篇

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

 王金平, 杜金元   

  1. 1School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China 2Department of Mathematics, Hubei Normal University, Huangshi 435002, China
  • 出版日期:2002-07-15 发布日期:2002-07-15
  • 基金资助:

    Supported by the NNSF of China, RFDP of Higher Education

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

摘要:

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.

关键词: Radon transform, projection-slice theorem, singular value decomposition

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

中图分类号: 

  • 44A15