Quantitative study on exact reconstruction sampling condition by verifying solution uniqueness in limited-view CT |
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| Affiliation: | 1. Sino-Dutch Biomedical & Information Engineering School, Northeastern University, China;2. School of Computer Science & Engineering, Northeastern University, China;3. Beijing Daheng Medical Equipment Co., Ltd., Chinese Academy of Sciences, China;1. School of Economics and Management, Beijing Jiaotong University, Beijing, 100044, China;2. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China;1. Key Laboratory of Ministry of Education for Advanced Display and System Application, Shanghai University, Shanghai 200072, China;2. School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China;1. Gas Sensors & Sensing Tehcnology Lab, The Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, PR China;2. The Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211, PR China;3. Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo, Zhejiang 315201, China;1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, China;2. School of Computer Science, Shanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai, China |
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| Abstract: | In limited-view computed tomography reconstruction, iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, inspired by compressive sensing, potentially claims large reductions in sampling requirements. However, a quantitative notion of this claim is non-trivial because of the ill-defined reduction in sampling achieved by the sparsity-exploiting method. In this paper, exact reconstruction sampling condition for limited-view problem is studied by verifying the uniqueness of solution in TV minimization model. Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness. Through this method, the sufficient sampling number of exact reconstruction is quantified for any fixed phantom and settled geometrical parameter in the limited-view problem. This paper provides a reference to quantify the sampling condition. Three phantoms are tested to study the sampling condition of limited view exact reconstruction in this paper. The experiment results show the quantified sampling number and indicate that an object would be accurately reconstructed as the scanning range becomes narrower by increasing sampling number. The increased samplings compensate for the deficiency of the projection angle. However, the lower bound of the scanning range corresponding to three different phantoms are presented, in which an exact reconstruction cannot be obtained once the projection angular is narrowed to this extent no matter how to increase sampling. |
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| Keywords: | Computed tomography Limited-view exact reconstruction Quantitative sampling Lower bound |
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