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Proceedings Paper

High order total variation method for interior tomography
Author(s): Jiansheng Yang; Hengyong Yu; Wenxiang Cong; Ming Jiang; Ge Wang
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Paper Abstract

While classic CT theory targets exact reconstruction of a whole cross-section or an entire object, practical applications often focus on a region of interest (ROI). The long-standing interior problem is well known that an internal ROI cannot be exactly reconstruct only from truncated projection data associated with x-rays through the ROI. Although lambda tomography was developed to target gradient-like features of an internal ROI for the interior problem, it has not been well accepted in the biomedical community. On the other hand, approximate local reconstruction methods are subject to biases and artifacts. Recently, the interior problem is re-visited with appropriate prior knowledge, delivering practical results. First, the interior problem can be exactly and stably solved if a sub-region in an ROI is known. Thereafter, the sub-region knowledge can be replaced by certain rather weak constraints. For local reconstruction, a candidate image can be represented as the sum of the truth and an ambiguity component. Very surprisingly, the ROI image is prove to be the unique minimizer of the total variation (TV) or high order total variation (HOT) functional subject to the measurement, if the ROI is piece-wise constant or polynomial. Interior tomography algorithms based on HOT minimization have been developed for x-ray CT, and then extended for interior SPECT and interior differential phasecontrast tomography, respectively. In this paper, we will summarize the main theoretical and algorithmic results.

Paper Details

Date Published: 17 October 2012
PDF: 8 pages
Proc. SPIE 8506, Developments in X-Ray Tomography VIII, 85061B (17 October 2012); doi: 10.1117/12.929123
Show Author Affiliations
Jiansheng Yang, Peking Univ. (China)
Hengyong Yu, Virginia Polytechnic Insitute and State Univ (United States)
Wake Forest Univ. School of Medicine (United States)
Wenxiang Cong, Virginia Polytechnic Institute and State Univ. (United States)
Ming Jiang, Peking Univ. (China)
Virginia Polytechnic Institute and State Univ. (United States)
Ge Wang, Virginia Polytechnic Institute and State Univ. (United States)
Wake Forest Univ. School of Medicine (United States)

Published in SPIE Proceedings Vol. 8506:
Developments in X-Ray Tomography VIII
Stuart R. Stock, Editor(s)

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