OPTIMAL RECOVERY OF A RADIATING SOURCE WITH MULTIPLE FREQUENCIES ALONG ONE LINE

被引：1

作者：

Brander, Tommi ^{[1
,2
]}

Ilmavirta, Joonas ^{[3
]}

Piiroinen, Petteri ^{[4
]}

Tyni, Teemu ^{[5
]}

机构：

[1] NTNU Norwegian Univ Sci & Technol, Fac Informat Technol & Elect Engn, Dept Math Sci, Trondheim, Norway

[2] Tech Univ Denmark, Dept Appl Math & Comp Sci, Lyngby, Denmark

[3] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, FI-40014 Jyvaskyla, Finland

[4] Univ Helsinki, Dept Math & Stat, PO 68,Pietari Kalmin Katu 5, Helsinki 00014, Finland

[5] Univ Oulu, Dept Math Sci, POB 3000, FI-90014 Oulu, Finland

来源：

INVERSE PROBLEMS AND IMAGING | 2020年 / 14卷 / 06期

基金：

芬兰科学院;

关键词：

inverse source problem; multispectral; SPECT; Laplace transform; beam hardening; multiplicative system theorem; attenuated Radon transform; uniqueness theorem; PET; emission computed tomography; nuclear medicine; TENSOR TOMOGRAPHY; RAY; INVERSION;

D O I：

10.3934/ipi.2020044

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.

引用

页码：967 / 983

页数：17

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