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Volumn 38, Issue SUPPL.1, 2011, Pages

Gel'fand-Graev's reconstruction formula in the 3D real space

Author keywords

backprojection filtration (BPF); computed tomography (CT); differential backprojection (DBP); image reconstruction; pseudo differential operator; x ray transform

Indexed keywords

IMAGE RECONSTRUCTION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; X RAYS;

EID: 79960917506     PISSN: 00942405     EISSN: None     Source Type: Journal    
DOI: 10.1118/1.3577765     Document Type: Conference Paper
Times cited : (8)

References (31)
  • 1
    • 33744522312 scopus 로고
    • Crofton function and inversion formulas in real integral geometry
    • 10.1007/BF01090671
    • I. M. Gel'fand and M. I. Graev, Crofton function and inversion formulas in real integral geometry., Funct. Anal. Appl. 25 (1), 1-5 (1991). 10.1007/BF01090671
    • (1991) Funct. Anal. Appl. , vol.25 , Issue.1 , pp. 1-5
    • Gel'Fand, I.M.1    Graev, M.I.2
  • 2
    • 0013514417 scopus 로고
    • Nonlocal inversion formulas in real integral geometry
    • 10.1007/BF01079461
    • I. M. Gel'fand and S. G. Gindikin, Nonlocal inversion formulas in real integral geometry., Funct. Anal. Appl. 11, 173-179 (1977). 10.1007/BF01079461
    • (1977) Funct. Anal. Appl. , vol.11 , pp. 173-179
    • Gel'Fand, I.M.1    Gindikin, S.G.2
  • 3
    • 79960896186 scopus 로고
    • Integral geometry on manifolds of k-dimensional planes
    • 10.1007/BF01075862
    • I. M. Gel'fand, M. I. Graev, and Z. Y. Shapiro, Integral geometry on manifolds of k-dimensional planes., Sov. Math. Dok. 7, 801-804 (1966). 10.1007/BF01075862
    • (1966) Sov. Math. Dok. , vol.7 , pp. 801-804
    • Gel'Fand, I.M.1    Graev, M.I.2    Shapiro, Z.Y.3
  • 5
    • 8744226637 scopus 로고    scopus 로고
    • An explicit inversion formula for the exponential Radon transform using data from 180°
    • H. Rullgard, An explicit inversion formula for the exponential radon transform using data from 180∼, Ark. Mat. 42, 353-362 (2004). 10.1007/BF02385485 (Pubitemid 39525751)
    • (2004) Arkiv for Matematik , vol.42 , Issue.2 , pp. 353-362
    • Rullgard, H.1
  • 8
    • 9744278198 scopus 로고    scopus 로고
    • An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT
    • DOI 10.1088/0031-9155/49/22/N02, PII S0031915504855659
    • Y. Zou and X. C. Pan, An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT., Phys. Biol. Med. 49 (22), N383-N387 (2004). 10.1088/0031-9155/49/22/N02 (Pubitemid 39585554)
    • (2004) Physics in Medicine and Biology , vol.49 , Issue.22
    • Zou, Y.1    Pan, X.2
  • 9
    • 11844249976 scopus 로고    scopus 로고
    • Cone-beam reconstruction using the backprojection of locally filtered projections
    • DOI 10.1109/TMI.2004.837794
    • J. D. Pack, F. Noo, and R. Clackdoyle, Cone-beam reconstruction using the backprojection of locally filtered projections., IEEE Trans. Med. Imag. 24 (1), 70-85 (2005). 10.1109/TMI.2004.837794 (Pubitemid 40088556)
    • (2005) IEEE Transactions on Medical Imaging , vol.24 , Issue.1 , pp. 70-85
    • Pack, J.D.1    Noo, F.2    Clackdoyle, R.3
  • 10
    • 37549028055 scopus 로고    scopus 로고
    • Scheme of computed tomography
    • Y. C. Wei, Scheme of computed tomography., J. X-ray Sci. Technol. 15 (4), 235-270 (2007).
    • (2007) J. X-ray Sci. Technol. , vol.15 , Issue.4 , pp. 235-270
    • Wei, Y.C.1
  • 11
    • 4544351987 scopus 로고    scopus 로고
    • A two-step Hilbert transform method for 2D image reconstruction
    • DOI 10.1088/0031-9155/49/17/006, PII S0031915504781828
    • F. Noo, R. Clackdoyle, and J. D. Pack, A two-step Hilbert transform method for 2D image reconstruction., Phys. Biol. Med. 49 (17), 3903-3923 (2004). 10.1088/0031-9155/49/17/006 (Pubitemid 39242984)
    • (2004) Physics in Medicine and Biology , vol.49 , Issue.17 , pp. 3903-3923
    • Noo, F.1    Clackdoyle, R.2    Pack, J.D.3
  • 12
    • 33744550629 scopus 로고    scopus 로고
    • Truncated Hilbert transform and image reconstruction from limited tomographic data
    • DOI 10.1088/0266-5611/22/3/019, PII S0266561106156208
    • M. Defrise, F. Noo, R. Clackdoyle, and H. Kudo, Truncated Hilbert transform and image reconstruction from limited tomographic data., Inverse Probl. 22 (3), 1037-1053 (2006). 10.1088/0266-5611/22/3/019 (Pubitemid 43814744)
    • (2006) Inverse Problems , vol.22 , Issue.3 , pp. 1037-1053
    • Defrise, M.1    Noo, F.2    Clackdoyle, R.3    Kudo, H.4
  • 13
    • 13244255699 scopus 로고    scopus 로고
    • Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan
    • DOI 10.1088/0031-9155/50/1/002
    • Y. Zou, X. C. Pan, and E. Y. Sidky, Image reconstruction in regions-of-interest from truncated projections in a reduced fan-beam scan., Phys. Biol. Med. 50 (1), 13-27 (2005). 10.1088/0031-9155/50/1/002 (Pubitemid 40185397)
    • (2005) Physics in Medicine and Biology , vol.50 , Issue.1 , pp. 13-27
    • Zou, Y.1    Pan, X.2    Sidky, E.Y.3
  • 14
    • 38749116981 scopus 로고    scopus 로고
    • A general local reconstruction approach based on a truncated hilbert transform
    • DOI 10.1155/2007/63634, PII S1687418807636340
    • Y. B. Ye, H. Y. Yu, Y. C. Wei, and G. Wang, A general local reconstruction approach based on a truncated Hilbert transform., Int. J. Biomed. Imag. 2007 (2007). 10.1155/2007/63634 (Pubitemid 351184563)
    • (2007) International Journal of Biomedical Imaging , vol.2007 , pp. 63634
    • Ye, Y.1    Yu, H.2    Wei, Y.3    Wang, G.4
  • 15
    • 40049084056 scopus 로고    scopus 로고
    • Exact interior reconstruction with cone-beam CT
    • DOI 10.1155/2007/10693, PII S1687418807106937
    • Y. B. Ye, H. Y. Yu, and G. Wang, Exact interior reconstruction with cone-beam CT., Int. J. Biomed. Imag. 2007 (2007). 10.1155/2007/10693 (Pubitemid 351445942)
    • (2007) International Journal of Biomedical Imaging , vol.2007 , pp. 10693
    • Ye, Y.1    Yu, H.2    Wang, G.3
  • 16
    • 56249107008 scopus 로고    scopus 로고
    • Local reconstruction using the truncated Hilbert transform via singular value decomposition
    • H. Y. Yu, Y. B. Ye, and G. Wang, Local reconstruction using the truncated Hilbert transform via singular value decomposition., J. X-Ray Sci. Technol. 16 (4), 243-251 (2008).
    • (2008) J. X-Ray Sci. Technol. , vol.16 , Issue.4 , pp. 243-251
    • Yu, H.Y.1    Ye, Y.B.2    Wang, G.3
  • 17
    • 42449133835 scopus 로고    scopus 로고
    • Tiny a priori knowledge solves the interior problem in computed tomography
    • DOI 10.1088/0031-9155/53/9/001, PII S0031915508723194
    • H. Kudo, Tiny a priori knowledge solves the interior problem in computed tomography., Phys. Biol. Med. 53 (9), 2207-2231 (2008). 10.1088/0031-9155/53/9/ 001 (Pubitemid 351570907)
    • (2008) Physics in Medicine and Biology , vol.53 , Issue.9 , pp. 2207-2231
    • Kudo, H.1    Courdurier, M.2    Noo, F.3    Defrise, M.4
  • 18
    • 62649137658 scopus 로고    scopus 로고
    • Solving the interior problem of computed tomography using a priori knowledge
    • 10.1088/0266-5611/24/6/065001
    • M. Courdurier, Solving the interior problem of computed tomography using a priori knowledge., Inverse Prob. 24, 065001 (2008). 10.1088/0266-5611/24/6/ 065001
    • (2008) Inverse Prob. , vol.24 , pp. 065001
    • Courdurier, M.1
  • 19
    • 43949102371 scopus 로고    scopus 로고
    • Exact interior reconstruction from truncated limited-angle projection data
    • DOI 10.1155/2008/427989
    • Y. B. Ye, H. Y. Yu, and G. Wang, Exact interior reconstruction from truncated limited-angle projection data., Int. J. Biomed. Imag. 427989 (2008). 10.1155/2008/427989 (Pubitemid 351703627)
    • (2008) International Journal of Biomedical Imaging , vol.2008 , Issue.1 , pp. 427989
    • Ye, Y.1    Yu, H.2    Wang, G.3
  • 20
    • 34247503333 scopus 로고    scopus 로고
    • Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning
    • DOI 10.1088/0031-9155/52/6/R01, PII S0031915507339456, R01
    • G. Wang, Y. B. Ye, and H. Y. Yu, Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning., Phys. Med. Biol. 52 (6), R1-R13 (2007). 10.1088/0031-9155/52/6/R01 (Pubitemid 46646382)
    • (2007) Physics in Medicine and Biology , vol.52 , Issue.6
    • Wang, G.1    Ye, Y.2    Yu, H.3
  • 23
    • 0343272676 scopus 로고
    • Die losungen der integralgleichung under deren anwendung in der tragflugeltheorie
    • 10.1007/BF01580284
    • H. Soehngen, Die losungen der integralgleichung under deren anwendung in der tragflugeltheorie., Math. Z. 45, 245-264 (1939). 10.1007/BF01580284
    • (1939) Math. Z. , vol.45 , pp. 245-264
    • Soehngen, H.1
  • 24
    • 0012721601 scopus 로고
    • On the finite Hilbert transform
    • 10.1093/qmath/2.1.199
    • F. G. Tricomi, On the finite Hilbert transform., Q. J. Math. 2 (1), 199-211 (1951). 10.1093/qmath/2.1.199
    • (1951) Q. J. Math. , vol.2 , Issue.1 , pp. 199-211
    • Tricomi, F.G.1
  • 25
    • 25144440411 scopus 로고    scopus 로고
    • A general exact reconstruction for cone-beam CT via backprojection- filtration
    • DOI 10.1109/TMI.2005.853626
    • Y. B. Ye, S. Y. Zhao, H. Y. Yu, and G. Wang, A general exact reconstruction for cone-beam CT via backprojection-filtration., IEEE Trans. Med. Imag. 24 (9), 1190-1198 (2005). 10.1109/TMI.2005.853626 (Pubitemid 41337158)
    • (2005) IEEE Transactions on Medical Imaging , vol.24 , Issue.9 , pp. 1190-1198
    • Ye, Y.1    Zhao, S.2    Yu, H.3    Wang, G.4
  • 26
    • 21144439799 scopus 로고    scopus 로고
    • A unified framework for exact cone-beam reconstruction formulas
    • DOI 10.1118/1.1869632
    • S. Y. Zhao, H. Y. Yu, and G. Wang, A unified framework for exact cone-beam reconstruction formulas., Med. Phys. 32 (6), 1712-1721 (2005). 10.1118/1.1869632 (Pubitemid 40880564)
    • (2005) Medical Physics , vol.32 , Issue.6 , pp. 1712-1721
    • Zhao, S.1    Yu, H.2    Wang, G.3
  • 27
    • 12744260178 scopus 로고    scopus 로고
    • Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data
    • 10.1088/0031-9155/49/24/007
    • T. L. Zhuang, Fan-beam and cone-beam image reconstruction via filtering the backprojection image of differentiated projection data., Phys. Bio. Med. 49 (24), 5489-5503 (2004). 10.1088/0031-9155/49/24/007
    • (2004) Phys. Bio. Med. , vol.49 , Issue.24 , pp. 5489-5503
    • Zhuang, T.L.1
  • 28
    • 1642569142 scopus 로고    scopus 로고
    • Exact image reconstruction on PI-lines from minimum data in helical cone-beam CT
    • DOI 10.1088/0031-9155/49/6/006, PII S0031915504730043
    • Y. Zou and X. C. Pan, Exact image reconstruction on PI-lines from minimum data in helical cone-beam., Phys. Bio. Med. 49 (6), 941-959, (2004). 10.1088/0031-9155/49/6/006 (Pubitemid 38401110)
    • (2004) Physics in Medicine and Biology , vol.49 , Issue.6 , pp. 941-959
    • Zou, Y.1    Pan, X.2
  • 30
    • 0042903710 scopus 로고    scopus 로고
    • A general scheme for constructing inversion algorithms for cone beam CT
    • DOI 10.1155/S0161171203209315
    • A. Katsevich, A general scheme for constructing inversion algorithms for cone-beam CT., Int. J. of Math. and Math. Sci. 21, 1305-1321 (2003). 10.1155/S0161171203209315 (Pubitemid 40587806)
    • (2003) International Journal of Mathematics and Mathematical Sciences , vol.2003 , Issue.21 , pp. 1305-1321
    • Katsevich, A.1
  • 31
    • 33645324031 scopus 로고    scopus 로고
    • Improved cone beam local tomography
    • 10.1088/0266-5611/22/2/015
    • A. Katsevich, Improved cone beam local tomography., Inverse Probl. 22 (2), 627-643 (2006). 10.1088/0266-5611/22/2/015
    • (2006) Inverse Probl. , vol.22 , Issue.2 , pp. 627-643
    • Katsevich, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.