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International Journal of Biomedical Imaging
Volume 2009 (2009), Article ID 125871, 3 pages
A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography
1Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
2Biomedical Imaging Division, VT-WFU School of Biomedical Engineering and Sciences, Virginia Tech, Blacksburg, VA 24061, USA
Received 7 September 2009; Accepted 1 November 2009
Academic Editor: Guowei Wei
Copyright © 2009 Weimin Han et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [17 citations]
The following is the list of published articles that have cited the current article.
- Jiansheng Yang, Hengyong Yu, Ming Jiang, and Ge Wang, “High-order total variation minimization for interior tomography,” Inverse Problems, vol. 26, no. 3, pp. 035013, 2010.
- Serge L. Shishkin, Hongcheng Wang, and Gregory S. Hagen, “Total variation minimization with separable sensing operator,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6134, pp. 86–93, 2010.
- Baodong Liu, Ge Wang, Erik L Ritman, Guohua Cao, Jianping Lu, Otto Zhou, Li Zeng, and Hengyong Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Physics in Medicine and Biology, vol. 56, no. 19, pp. 6337–6357, 2011.
- Qiong Xu, Xuanqin Mou, Ge Wang, Jered Sieren, Eric A. Hoffman, and Hengyong Yu, “Statistical Interior Tomography,” Ieee Transactions on Medical Imaging, vol. 30, no. 5, pp. 1116–1128, 2011.
- Jiansheng Yang, Hengyong Yu, Ming Jiang, and Ge Wang, “High-order total variation minimization for interior SPECT,” Inverse Problems, vol. 28, no. 1, pp. 015001, 2011.
- Hengyong Yu, Ge Wang, Jiang Hsieh, Daniel W. Entrikin, Sandra Ellis, Baodong Liu, and John Jeffrey Carr, “Compressive Sensing-Based Interior Tomography: Preliminary Clinical Application,” Journal Of Computer Assisted Tomography, vol. 35, no. 6, pp. 762–764, 2011.
- Esther Klann, “A Mumford–Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography,” SIAM Journal on Imaging Sciences, vol. 4, no. 4, pp. 1029–1048, 2011.
- Katsuyuki Taguchi, Jingyan Xu, Somesh Srivastava, Benjamin M. W. Tsui, Jochen Cammin, and Qiulin Tang, “Interior region-of-interest reconstruction using a small, nearly piecewise constant subregion,” Medical Physics, vol. 38, no. 3, pp. 1307, 2011.
- Ge Wang, Jie Zhang, Hao Gao, Victor Weir, Hengyong Yu, Wenxiang Cong, Xiaochen Xu, Haiou Shen, James Bennett, Mark Furth, Yue Wang, and Michael Vannier, “Towards Omni-Tomography-Grand Fusion of Multiple Modalities for Simultaneous Interior Tomography,” Plos One, vol. 7, no. 6, 2012.
- E. Katsevich, A. Katsevich, and G. Wang, “Stability of the interior problem with polynomial attenuation in the region of interest,” Inverse Problems, vol. 28, no. 6, 2012.
- Wenxiang Cong, Jiangsheng Yang, and Ge Wang, “Differential phase-contrast interior tomography,” Physics in Medicine and Biology, vol. 57, no. 10, pp. 2905–2914, 2012.
- Pascal Thériault Lauzier, Jie Tang, and Guang-Hong Chen, “Time-resolved cardiac interventional cone-beam CT reconstruction from fully truncated projections using the prior image constrained compressed sensing (PICCS) algorithm,” Physics in Medicine and Biology, vol. 57, no. 9, pp. 2461–2476, 2012.
- Ge Wang, and Hengyong Yu, “The meaning of interior tomography,” Physics in Medicine and Biology, vol. 58, no. 16, pp. R161–R186, 2013.
- Ge Wang, Mannudeep Kalra, Venkatesh Murugan, Yan Xi, Lars Gjesteby, Matthew Getzin, Qingsong Yang, Wenxiang Cong, and Michael Vannier, “Vision 20/20: Simultaneous CT-MRI — Next chapter of multimodality imaging,” Medical Physics, vol. 42, no. 10, pp. 5879–5889, 2015.
- Minji Lee, Yoseob Han, John Paul Ward, Michael Unser, and Jong Chul Ye, “Interior Tomography Using 1D Generalized Total Variation. Part II: Multiscale Implementation,” SIAM Journal on Imaging Sciences, vol. 8, no. 4, pp. 2452–2486, 2015.
- Esther Klann, Eric Todd Quinto, and Ronny Ramlau, “Wavelet methods for a weighted sparsity penalty for region of interest tomography,” Inverse Problems, vol. 31, no. 2, pp. 025001, 2015.
- Hengyong Yu, Ge Wang, Jiansheng Yang, Jed D. Pack, Ming Jiang, and Bruno De Man, “Data consistency condition for truncated projections in fan-beam geometry,” Journal Of X-Ray Science And Technology, vol. 23, no. 5, pp. 627–638, 2015.