THE SPHERE METHOD FOR THE INVERSE PROBLEMS OF THE RADON TRANSFORMS

被引：0

作者：

Yu, Yufeng ^{[1
]}

机构：

[1] Shanxi Normal Univ, Sch Math & Comp Sci, Linfen 041000, Shanxi, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2020年 / 51卷 / 03期

关键词：

Radon transform; inverse problems; the sphere method;

D O I：

10.1007/s13226-020-0449-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using a different method - the sphere method, which is based on the technique of changing the integral on a plane into the integral on a hemisphere, we give some concise inverse formulas of the Radon transforms of functions with support in a cone with vertex at the origin and flare angle less than pi/2, or with compact support. These formulas are easy for the computer to operate and thus can be applied in the imaging techniques of computerized tomography.

引用

页码：1053 / 1063

页数：11

共 13 条

[1] Deans SR., 1983, The Radon Transform and Some of its Applications
[2] Gardner RJ., 2006, Encyclopedia of Mathematics and its Applications, V2
[3] Helgason S., 1999, The Radon transform, Vvol 2, DOI DOI 10.1007/978-1-4757-1463-0
[4] Helgason Sigurdur, 1965, ACTA MATH, V113, P153, DOI 10.1007/BF02391776
[5] Markoe A, 2006, ANAL TOMOGRAPHY ENCY
[6] Natterer F., 1986, The Mathematics of Computerized Tomography
[7] MAPPING PROPERTIES OF THE RADON-TRANSFORM
OBERLIN, DM
STEIN, EM
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1982, 31 (05) : 641 - 650
[8] THE INVERTIBILITY OF ROTATION INVARIANT RADON TRANSFORMS
QUINTO, ET
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1983, 91 (02) : 510 - 522
[9] Reconstruction of functions from their integrals over k-planes
Rubin, B
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2004, 141 (1) : 93 - 117
[10] Convolution-backprojection method for the k-plane transform, and Calderon's identity for ridgelet transforms
Rubin, B
[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2004, 16 (03) : 231 - 242

← 1 2 →