A note on singular value decomposition for radon transform in Rn

被引：14

作者：

Wang, JP

Du, JY

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Hubei Normal Univ, Dept Math, Huangshi 435002, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2002年 / 22卷 / 03期

关键词：

radon transform; projection-slice theorem; singular value decomposition;

D O I：

10.1016/S0252-9602(17)30300-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 R-n with respect to the weight W-lambda(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.

引用

页码：311 / 318

页数：8

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