Adjoint State Method for the Identification Problem in SPECT: Recovery of Both the Source and the Attenuation in the Attenuated X-Ray Transform

被引：8

作者：

Luo, Songting ^{[1
]}

Qian, Jianliang ^{[2
]}

Stefanov, Plamen ^{[3
]}

机构：

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[3] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2014年 / 7卷 / 02期

基金：

美国国家科学基金会;

关键词：

single-photon emission computerized tomography; X-ray transform; adjoint state method; fast sweeping method; wave front set; uniqueness; stability; COMPUTERIZED-TOMOGRAPHY; RECONSTRUCTION; MAP;

D O I：

10.1137/130939559

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply efficient fast sweeping methods to solve static transport equations and adjoint state equations. Numerous examples are presented to demonstrate various features of the identification problem, such as uniqueness and nonuniqueness, stability and instability, and recovery of the wave front set.

引用

页码：696 / 715

页数：20