| A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R~n |
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| 作者姓名： | 王金平 杜金元 |
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| 作者单位： | Wang Jinping Du JinyuanSchool of Mathematics and Statistics，Wuhan University，Wuhan 430072，ChinaDepartment of Mathematics，Hubei Normal University，Huangshi 435002，China |
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| 基金项目： | the NNSF of China，RFDP of Higher Education |
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| 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 Wλ(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.
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A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN Rn |
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| Wang Jinping Du JinyuanSchool of Mathematics and Statistics,Wuhan University,Wuhan ,China.A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R~n[J].Acta Mathematica Scientia,2002,22(3). |
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| Authors: | Wang Jinping Du JinyuanSchool of Mathematics and Statistics Wuhan University Wuhan China |
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| Institution: | Wang Jinping Du JinyuanSchool of Mathematics and Statistics,Wuhan University,Wuhan 430072,ChinaDepartment of Mathematics,Hubei Normal University,Huangshi 435002,China |
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| 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. |
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| Keywords: | Radon transform projection-slice theorem singular value decomposition |
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