An inversion formula for the attenuated X-ray transformation

被引：24

作者：

Novikov, RG ^{[1
]}

机构：

[1] Univ Nantes, CNRS, UMR 6629, Dept Math, F-44322 Nantes 03, France

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 2001年 / 332卷 / 12期

关键词：

D O I：

10.1016/S0764-4442(01)01965-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The problem of inversion of the attenuated X-ray transformation P-alpha is solved by an explicit formula. The problem of range characterization for P-alpha in dimension 2 is solved (on a preliminary level) by other explicit formula. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

引用

页码：1059 / 1063

页数：5

共 50 条

[1] An inversion formula for the attenuated X-ray transformation
Novikov, RG
ARKIV FOR MATEMATIK, 2002, 40 (01): : 145 - 167
[2] FOURIER INVERSION OF THE ATTENUATED X-RAY TRANSFORM
MARKOE, A
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1984, 15 (04) : 718 - 722
[3] An inversion method for an attenuated x-ray transform
Palamodov, VP
INVERSE PROBLEMS, 1996, 12 (05) : 717 - 729
[4] Inversion of the Attenuated X-Ray Transforms: Method of Riesz Potentials
Yu, Yufeng
JOURNAL OF FUNCTION SPACES, 2020, 2020
[5] Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Acad. Koptyug prosp. 4, 630090 Novosibirsk, Russia
不详
J Inverse Ill Posed Probl, 2007, 7 (735-765):
[6] Inversion of the scalar and vector attenuated X-ray transforms in a unit disc
Kazantsev, S.G.
Bukhgeim, A.A.
Journal of Inverse and Ill-Posed Problems, 2007, 15 (07): : 735 - 765
[7] On the range characterization for the two-dimensional attenuated x-ray transformation
Novikov, RG
INVERSE PROBLEMS, 2002, 18 (03) : 677 - 700
[8] Inversion of the attenuated X-ray transforms-Method of convolution-backprojection
Yu, Yufeng
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2021, 54 : 345 - 365
[9] Inversion formula for the non-uniformly attenuated x-ray transform for emission imaging in R3 using quaternionic analysis
Fathi, S. M. Saberi
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (33)
[10] PARTIAL INVERSION OF THE 2D ATTENUATED X-RAY TRANSFORM WITH DATA ON AN ARC
Fujiwara, Hiroshi
Sadiq, Kamran
Tamasan, Alexandru
INVERSE PROBLEMS AND IMAGING, 2022, 16 (01) : 215 - 228

← 1 2 3 4 5 →