High-order total variation minimization for interior tomography

被引：117
|
作者：
Yang, Jiansheng [1 ,2 ]
Yu, Hengyong [2 ]
Jiang, Ming [1 ,2 ]
Wang, Ge [2 ]
机构：
[1] Peking Univ, LMAM, Sch Math Sci, Beijing 100871, Peoples R China
[2] Virginia Tech, Biomed Imaging Div, VT WFU Sch Biomed Engn & Sci, Blacksburg, VA 24061 USA
来源：
INVERSE PROBLEMS | 2010年 / 26卷 / 03期
关键词：
RADON-TRANSFORM; RECONSTRUCTION; FORMULA;
D O I：
10.1088/0266-5611/26/3/035013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, an accurate solution to the interior problem was proposed based on the total variation (TV) minimization, assuming that a region of interest (ROI) is piecewise constant. In this paper, we generalize that assumption to allow a piecewise polynomial ROI, introduce the high-order TV (HOT), and prove that an ROI can be accurately reconstructed from projection data associated with x-rays through the ROI via the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation.
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收藏
页数：29
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