| Title | Initial analysis of the middle problem in CT image reconstruction |
| Authors | Yang, Jiansheng Yu, Hengyong Wang, Ge |
| Affiliation | Peking Univ, Sch Math Sci, LMAM, Beijing, Peoples R China. Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing, Peoples R China. Rensselaer Polytech Inst, CBIS, Biomed Imaging Ctr Cluster, Troy, NY USA. Univ Massachusetts Lowell, Dept Elect & Comp Engn, Lowell, MA USA. Peking Univ, Sch Math Sci, LMAM, Beijing, Peoples R China. Yang, JS (reprint author), Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing, Peoples R China. Yang, JS Wang, G (reprint author), Rensselaer Polytech Inst, CBIS, Biomed Imaging Ctr Cluster, Troy, NY USA. Yu, HY (reprint author), Univ Massachusetts Lowell, Dept Elect & Comp Engn, Lowell, MA USA. |
| Keywords | Middle problem middle tomography data truncation limited-angle tomography image reconstruction POCS GRATING INTERFEROMETER INTERIOR TOMOGRAPHY |
| Issue Date | 2017 |
| Publisher | JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY |
| Citation | JOURNAL OF X-RAY SCIENCE AND TECHNOLOGY.2017,25(4),547-559. |
| Abstract | The interior and exterior problems have been extensively studied in the field of reconstruction of computed tomography (CT) images, which lead to important theoretical and practical results. In this study, we formulate a middle problem of CT image reconstruction, which is more challenging than either the interior or exterior problems. In the middle problem of CT image reconstruction, projection data are measured through and only through the middle dough-like region, so that each projection profile misses data not only internally but also on both sides. For an object with a radially symmetric exterior, we proved that the middle problem could be uniquely solved if the middle ring-shaped zone is piecewise constant or there is a known sub-region inside this middle region. Then, we designed and evaluated a POCS-based algorithm for middle tomography, which is to reconstruct a middle image only from the available data. Finally, the remaining issues are also discussed for further research. |
| URI | http://hdl.handle.net/20.500.11897/475838 |
| ISSN | 0895-3996 |
| DOI | 10.3233/XST-16211 |
| Indexed | SCI(E) |
| Appears in Collections: | 数学科学学院 数学及其应用教育部重点实验室 |
