A general region-of-interest image reconstruction approach with truncated Hilbert transform

Journal of X-Ray Science and Technology

Volumn 17, Issue 2, 2009, Pages 135-152

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

^a TSINGHUA UNIVERSITY   (China)

Author keywords

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

Indexed keywords

APRIORI; COMPUTED TOMOGRAPHY (CT); DATA SETS; DATA SUFFICIENCY CONDITION; DIFFERENTIATED BACKPROJECTION; GOOD STABILITY; INTERIOR PROBLEM; LINE INTEGRALS; PROJECTION ONTO CONVEX SETS; RECONSTRUCTION ALGORITHMS; REGION OF INTEREST; REGION-OF-INTEREST (ROI); REGION-OF-INTEREST IMAGES; ROI RECONSTRUCTION; SMALL REGION; TRUNCATED HILBERT TRANSFORM; TRUNCATED HILBERT TRANSFORMS;

COMPUTERIZED TOMOGRAPHY; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL TRANSFORMATIONS; REPAIR; SET THEORY;

IMAGE RECONSTRUCTION;

ALGORITHM; ARTICLE; COMPUTER ASSISTED TOMOGRAPHY; COMPUTER SIMULATION; IMAGE PROCESSING; IMAGE QUALITY; METHODOLOGY;

ALGORITHMS; COMPUTER SIMULATION; IMAGE PROCESSING, COMPUTER-ASSISTED; PHANTOMS, IMAGING; TOMOGRAPHY, X-RAY COMPUTED;

EID: 69549116783     PISSN: 08953996     EISSN: None     Source Type: Journal    
DOI: 10.3233/XST-2009-0218     Document Type: Article

References (32)

1. F. Natterer, The Mathematics of Computerized Tomography, New York: Wiley, 1986.
2. E.T. Quinto, Tomographic reconstructions from incomplete data-numerical inversion of the exterior Radon transform, Inverse Problems 4 (1988), 867-876.
3. A. Faridani, E.L. Ritman and K.T. Smith, Local tomography, SIAM J Appl Math 52 (1992), 459-484.
4. A.I. Katsevich and A.G. Ramm, Pseudolocal tomography, SIAM J Appl Math 56 (1996), 167-191.
5. Y.B. Ye, H.Y Yu and G. Wang, Cone-beam pseudo-lambda tomography, Inverse Problems 23 (2007), 203-215.
6. F. Noo, M. Defrise, R. Clackdoyle and H. Kudo, Image reconstruction from fan-beam projections on less than a short scan, Phys Med Biol 47 (2002), 2525-2546.
7. I.M. Gelfand and M.I. Graev, Crofton's function and inversion formulas in real integral geometry, Funct Anal Appl 25 (1991), 1-5.
8. Y Zou and X. Pan, Exact image reconstruction on PI-line from minimum data in helical cone-beam CT, Phys Med Biol 49 (2004), 941-959.
9. R. Clackdoyle, F. Noo, J. Guo and J. Roberts, A quantitative reconstruction from truncated projections in classical tomography, IEEE Trans Nucl Sci 51 (2004), 2570-2578.
10. F. Noo, R. Clackdoyle and J.D. Pack, A two-step Hilbert transform method for 2D image reconstruction, Phys Med Biol 49 (2004), 3903-3923.
11. T. Zhuang, S. Leng, B.E. Nett and G.-H. Chen, Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data, Phys Med Biol 49 (2004), 5489-5503.
12. Y. Zou, X. Pan and E.Y. Sidky, Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan, Phys Med Biol 50 (2005), 13-28.
13. L.F. Yu, Y Zou, E.Y. Sidky, C.A. Pelizzari, P. Munro and X. Pan, Region of Interest Reconstruction From Truncated Data in Circular Cone-Beam CT, IEEE Tran Med Imag 25(7) (2006), 869-881.
14. J.D. Pack, F. Noo and R. Clackdoyle, Cone-beam reconstruction using the backprojection of locally filtered projections, IEEE Trans Med Imag 24 (2005), 70-85.
15. Y Ye, S. Zhao, H.Y Yu and G. Wang, A general exact reconstruction for cone-beam CT via backprojectionfiltration, IEEE Trans Med Imag 24 (2005), 1190-1198.
16. L. Li, Z.Q. Chen, L. Zhang, Y.X. Xing and K.J. Kang, 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 65 (2007), 1041-1047.
17. F.G. Tricomi, Integral Equations, New York: Dover, 1957.
18. I.M. Gelfand and A.B. Goncharov, Recovery of a compactly supported function starting from its integrals over lines intersecting a given set of points in space, Soviet Math Dokl 34 (1987), 373-376.
19. M. Defrise, F. Noo, R. Clackdoyle and H. Kudo, Truncated Hilbert transform and image reconstruction from limited tomographic data, Inverse Problems 22 (2006), 1037-1053.
20. Y Ye, H.Y. Yu, Y Wei and G. Wang, A general local reconstruction approach based on a truncated Hilbert transform, Int J Biomed Imag 2007, Article ID: 63634, 2007.
21. H. Kudo, M. Courdurier, F. Noo and M. Defrise, Tiny a priori knowledge solves the interior problem in computed tomography, Phys Med Biol 53 (2008), 2207-2231.
22. L. Li, K.J. Kang, Z.Q. Chen 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.
23. A. Lars, Complex Analysis, (3rd ed.), McGraw Hill, 1979.
24. D.C. Youla and H. Webb, Image restoration by the method of convex projections: Part I. Theory, IEEE Trans Med Imag 1 (1982), 81-94.
25. L. Rudin, S. Osher and E. Fatemi, Nonlinear Total Variation based noise removal algorithms, Physica D 60 (1992), 259-268.
26. G.Q. Yu, L. Li, J. Gu and L. Zhang, Total Variation Based Iterative Image Reconstruction, Computer Vision for Biomedical Image Applications 3765 (2005), 526-534.
27. E. Candes, J. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Commun Pure Appl Math (2006), 1207-1223.
28. E.Y. Sidky, C.-M. Kao and X. Pan, Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT, J X-ray Sci Tech 14 (2006), 119-139.
29. G.-H. Chen, J. Tang and S. Leng, Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets, Med Phys 35 (2008), 660-663.
30. E.Y. Sidky and X. Pan, Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization, Phys Med Biol 53 (2008), 4777-4807.
31. L.A. Shepp and B.F. Logan, The Fourier reconstruction of a head section, IEEE Trans Nucl Sci 21 (1974), 21-43.
32. Y Ye, H.Y. Yu and G. Wang, Exact Interior Reconstruction from Truncated Limited-Angle Projection Data, Int J Biomed Imag 2008, Article ID: 427989, 2008.