Singular value decomposition for the truncated Hilbert transform: part II

被引：15
|
作者：
Katsevich, A. [1 ]
机构：
[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
来源：
INVERSE PROBLEMS | 2011年 / 27卷 / 07期
关键词：
IMAGE-RECONSTRUCTION;
D O I：
10.1088/0266-5611/27/7/075006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Hilbert transform is a very important tool in computed tomography. Image reconstruction from truncated tomographic data can be reduced to the problem of inverting the Hilbert transform (H-14 phi)(y) := 1/pi integral(a4)(a1) phi(x)/x-y dx = psi(y) knowing psi on the interval [a(2), a(3)], where a(1) < a(2) < a(3) < a(4). In this paper, we obtain a singular value decomposition for the operator H-14.
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页数：7
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