Recent advance in exact ROI/VOI image reconstruction

Current Medical Imaging Reviews

Volumn 6, Issue 2, 2010, Pages 112-118

  Li, Liang ^a,b   Chen, Zhiqiang ^a,b   Kang, Kejun ^a,b   Zhang, Li ^a,b   Xing, Yuxiang ^a,b  

^a TSINGHUA UNIVERSITY   (China)

^b KEY LABORATORY OF PARTICLE AND RADIATION IMAGING TSINGHUA UNIVERSITY   (China)

Author keywords

Computed tomography (CT); Image reconstruction; Interior problem; Region of interest (ROI); Truncated Hilbert transform

Indexed keywords

ALGORITHM; ARTICLE; CONE BEAM COMPUTED TOMOGRAPHY; IMAGE QUALITY; IMAGE RECONSTRUCTION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PRIORITY JOURNAL; RADIATION BEAM; RADIATION DETECTOR; RADIATION DOSE; RADIOGRAPHY;

EID: 77955807408     PISSN: 15734056     EISSN: None     Source Type: Journal    
DOI: 10.2174/157340510791268506     Document Type: Article

References (44)

1. Natterer F, The Mathematics of Computerized Tomography. New York: Wiley 1986.
2. E.T. Quinto, "Tomographic reconstructions from incomplete datanumerical inversion of the exterior Radon transform." Inverse Problems 1988; 4: 867-76.
3. Nassi M, BrodyWR, Medoff B P, et al. Iterative reconstructionreprojection: an algorithm for limited data cardiac-computed tomography. IEEE Trans Biomed Eng 1982; 29(5): 333-41.
4. Heffernan PB, Robb RA. Image reconstruction from incomplete projection data: Iterative reconstruction-reprojection techniques. IEEE Trans Biomed Eng 1983; 30(12): 838-41.
5. Kim JH, Kwak KY, Park SB, et al. Projection space iteration reconstruction- reprojection. IEEE Trans Med Imaging 1985; 4(3): 139-43.
6. Faridani A, Ritman EL, Smith KT. Local tomography. SIAM J Appl Math 1992; 52: 459-84.
7. Katsevich AI, Ramm AG, Pseudolocal tomography. SIAM J Appl Math 1996; 56: 167-91.
8. Ye YB, Yu HY, Wang G. Cone-beam pseudo-lambda tomography. Inverse Problems 2007; 23: 203-15.
9. Katsevich A. Theoretically exact filtered backprojection-type inversion algorithm for spiral CT. SIAM J Appl Math 62: 2012-26.
10. Katsevich A. A general scheme for constructing inversion algorithms for cone-beam CT. Int J Math Math Sci 2003; 21: 1305-21.
11. Noo F, Defrise M, Clackdoyle R, Kudo H. Image reconstruction from fan-beam projections on less than a short scan. Phys Med Biol 2002; 47: 2525-46.
12. Parker DL. Optimum short-scan convolution reconstruction for fanbeam CT. Med Phys 1982; 9: 254-7.
13. Kudo H, Noo F, Defrise M, Clackdoyle R. In: Norfolk VA, Ed. New super-short-scan algorithms for fan-beam and conebeam reconstruction Conference. Record of the 2002. IEEE Nuclear Science Symposium and Medical Imaging Conference 2003; pp: 902- 6.
14. Grangeat P. In: Herman GT, Louis AK, Natterer F, Eds. Mathematical framework of cone-beam 3D reconstruction via the first derivative of the Radon transform Mathematical Methods in Tomography. Lecture Notes in Mathematics. Berlin: Springer 1991; vol. 1497: pp. 66-97.
15. Zou Y and Pan X. Exact image reconstruction on PI-lines from minimum data in helical cone-beam CT. Phys Med Biol 2004; 49: 941-59.
16. Zou Y, Pan X. Image reconstruction on PI-lines by use of filtered backprojection in helical cone-beam CT. Phys Med Biol 2004; 49: 2717-31.
17. Danielsson PE, Edholm P, Eirksson J, et al. Towards exact 3Dreconstructin for helical cone-beam scanning of long objects: a new arrangement and a new completeness condition. International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (Nemacolin, PA), 1997; pp. 41-144.
18. Noo F, Clackdoyle R, Pack JD. A two-step Hilbert transform method for 2D image reconstruction. Phys Med Biol 2004; 49: 3903-23.
19. Zhuang T, Leng S, Nett BE, Chen G-H. Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data. Phys Med Biol 2004; 49: 5489-503.
20. Pack JD, Noo F, Clackdoyle R. Cone-beam reconstruction using the backprojection of locally filtered projections. IEEE Trans Med Imaging 2005; 24: 70-85.
21. Ye Y, Zhao S, Yu HY, Wang G. A general exact reconstruction for cone-beam CT via backprojectionfiltration. IEEE Trans Med Imaging 2005; 24: 1190-8.
22. Zou Y, Pan X, Sidky EY. Image reconstruction in regions-ofinterest from truncated projections in a reduced fan-beam scan. Phys Med Biol 2005; 50: 13-28.
23. Yu LF, Zou Y, Sidky EY, Pelizzari CA, Munro P, Pan X. Region of interest reconstruction from truncated data in circular cone-beam CT. IEEE Tran Med Imaging 2006; 25(7): 869-81.
24. Li L, Chen ZQ, Kang KJ, et al. Investigation of Exact Truncated Data Image Reconstruction Algorithm on Parallel PI-Line Segments in Fan-Beam Scans. Tsinghua Sci Technol 2007; 12: 337-44.
25. Gelfand IM, Graev MI. Crofton Function And Inversion Formulas In Real Integral Geometry. Funct Anal Appl 1991; 25(1): 1-5.
26. Rullgard H. An explicit inversion formula for the exponential Radon transform using data from 180o. Ark Mat 2004; 42: 353-62.
27. Tricomi FG. Integral Equations. New York: Dover 1957.
28. Gelfand IM, Goncharov AB. Recovery of a compactly supported function starting from its integrals over lines intersecting a given set of points in space. Soviet Math Dokl 1987; 34: 373-6.
29. Defrise M, Noo F, Clackdoyle R, Kudo H. Truncated Hilbert transform and image reconstruction from limited tomographic data. Inverse Problems 2006; 22: 1037-53.
30. Li L, Chen ZQ, Zhang L, et al. A cone-beam tomography system with a reduced size planar detector: a backprojection-filtration reconstruction algorithm as well as numerical and practical experiments. Appl Radiat Isotopes 2007; 65: 1041-7.
31. Leng S, Zhuang T, Nett BE, Chen G. Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector. Phys Med Biol 2005; 50: 1805-20.
32. Defrise M, Noo F, Clackdoyle R and Kudo H. Enlargement of the region of accurate reconstruction in computed tomography from truncated data. Proc. 8th Int. Conf. on Fully 3D Image Reconstruction in Radiology and Nuclear Medicine (Salt Lake City, USA), 2005; pp: 46-50.
33. Berenstein CA, Gay R. Complex Variables. An Introduction New York: Springer 1991.
34. Youla DC, Webb H. Image restoration by the method of alternating orthogonal projections: part I Theory. IEEE Trans Med Imaging 1982; 1: 81-94.
35. Lewitt RM. Processing of incomplete measurement data in computed tomography. Med Phys 1979; 6: 412-7.
36. Ye Y, Yu H, Wei Y, et al. A general local reconstruction approach based on a truncated hilbert transform. Int J Biomed Imaging Article ID 63634, 2007.
37. Kudo H, Courdurier M, Noo F, Defrise M. Tiny a priori knowledge solves the interior problem in computed tomography. Phys Med Biol 2008; 53: 2207-31.
38. Courdurier M, Noo F, Kudo H, et al. Solving the interior problem of computed tomography using a priori knowledge. Inverse Problem 2008; 24: 065001.
39. Yu H, Y Ye, Wang G, et al. Local reconstruction using the truncated hilbert transform via singular value decomposition. J X-Ray Sci Technol 2008; 16(4): 243-51.
40. Li L, Kang KJ, Chen ZQ, et al. 3D Region-of-Interest (ROI) Reconstruction from Truncated Data in Circular Cone-beam CT. Conference Record of 2008. IEEE Nuclear Science Symposium and Medical Imaging Conference. Dresden, Germany, Paper No M10- 346.
41. Li L, Kang KJ, Chen ZQ, et al. A General region-of-interest image reconstruction approach with truncated hilbert transform. J X-ray Sci Tech 2009; 17: 135-52.
42. Yu H, Wang G. Compressed sensing based Interior tomography. Phys Med Biol 2009; 54(9): 2791-805.
43. Quinto ET. Local algorithms in exterior tomography. J Comp Appl Math 2007; 199: 141-8.
44. Wang G, Yu H, DeMan B. An outlook on x-ray CT research and development. Med Phys 2008; 35: 1051-64.