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Volumn 8, Issue , 1999, Pages 107-141

Numerical methods in tomography

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EID: 85011519667     PISSN: 09624929     EISSN: 14740508     Source Type: Journal    
DOI: 10.1017/S0962492900002907     Document Type: Article
Times cited : (43)

References (56)
  • 2
    • 0000439725 scopus 로고
    • Row-action methods for huge and sparse systems and their applications
    • Censor Y. (1981), ‘Row-action methods for huge and sparse systems and their applications’, SIAM Review 23, 444–466.
    • (1981) SIAM Review , vol.23 , pp. 444-466
    • Censor, Y.1
  • 3
    • 0002206795 scopus 로고
    • Strong underrelaxation in Kaczmarz's method for inconsistent systems
    • Censor Y., Eggermont P. B. and Gordon D. (1983), ‘Strong underrelaxation in Kaczmarz's method for inconsistent systems’, Numer. Math. 41, 83–92.
    • (1983) Numer. Math. , vol.41 , pp. 83-92
    • Censor, Y.1    Eggermont, P.B.2    Gordon, D.3
  • 5
    • 0019047767 scopus 로고
    • A scientific study of filter selection for a fan-beam convolution algorithm
    • Chang L. T. and Herman G. T. (1980), ‘A scientific study of filter selection for a fan-beam convolution algorithm’, SIAM J. Appl. Math. 39, 83–105.
    • (1980) SIAM J. Appl. Math. , vol.39 , pp. 83-105
    • Chang, L.T.1    Herman, G.T.2
  • 6
    • 42149197029 scopus 로고
    • The circular harmonic Radon transform
    • Chapman C. H. and Cary P. W. (1986), ‘The circular harmonic Radon transform’, Inverse Problems 2, 23–49.
    • (1986) Inverse Problems , vol.2 , pp. 23-49
    • Chapman, C.H.1    Cary, P.W.2
  • 7
    • 0018921312 scopus 로고
    • Fully three-dimensional emission tomography
    • Colsher J. G. (1980), ‘Fully three-dimensional emission tomography’, Phys. Med. Biol. 25, 103–115.
    • (1980) Phys. Med. Biol. , vol.25 , pp. 103-115
    • Colsher, J.G.1
  • 8
    • 0001069532 scopus 로고
    • Representation of a function by its line integrals, with some radiological applications I
    • Cormack A. M. (1963), ‘Representation of a function by its line integrals, with some radiological applications I’, J. Appl. Phys. 34, 2722–2727.
    • (1963) J. Appl. Phys. , vol.34 , pp. 2722-2727
    • Cormack, A.M.1
  • 9
    • 12544260746 scopus 로고
    • Representation of a function by its line integrals, with some radiological applications II
    • Cormack A. M. (1964), ‘Representation of a function by its line integrals, with some radiological applications II’, J. Appl. Phys. 35, 195–207.
    • (1964) J. Appl. Phys. , vol.35 , pp. 195-207
    • Cormack, A.M.1
  • 11
    • 0024508539 scopus 로고
    • Three-dimensional image reconstruction from complete projections
    • Defrise M., Townsend D. W. and Clack R. (1989), ‘Three-dimensional image reconstruction from complete projections’, Phys. Med. Biol. 34, 573–587.
    • (1989) Phys. Med. Biol. , vol.34 , pp. 573-587
    • Defrise, M.1    Townsend, D.W.2    Clack, R.3
  • 12
    • 0028392621 scopus 로고
    • A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection
    • Defrise M. and Clack R. (1995), ‘A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection’, IEEE Trans. Med. Imag. 13, 186–195.
    • (1995) IEEE Trans. Med. Imag. , vol.13 , pp. 186-195
    • Defrise, M.1    Clack, R.2
  • 13
    • 85011481945 scopus 로고
    • Maximum likelihood from incomplete data via the EM algorithm
    • Dempster A. P., Laird N. M. and Rubin D. B. (1977), ‘Maximum likelihood from incomplete data via the EM algorithm’, J. R. Statist. Soc. B 39, 1–38.
    • (1977) J. R. Statist. Soc. B , vol.39 , pp. 1-38
    • Dempster, A.P.1    Laird, N.M.2    Rubin, D.B.3
  • 14
    • 0023669757 scopus 로고
    • Linograms in image reconstruction from projections
    • Edholm P. and Herman G. T. (1987), ‘Linograms in image reconstruction from projections’, IEEE Trans. Med. Imag. 6, 301–307.
    • (1987) IEEE Trans. Med. Imag. , vol.6 , pp. 301-307
    • Edholm, P.1    Herman, G.T.2
  • 17
    • 0013553757 scopus 로고
    • Recovery of a compactly supported function starting from its integrals over lines intersecting a given set of points in space
    • (1986); English Translation in Soviet Math. Dokl. 34, 373–376.
    • Gelfand I. M. and Goncharov A. B. (1987), ‘Recovery of a compactly supported function starting from its integrals over lines intersecting a given set of points in space’, Doklady 290 (1986); English Translation in Soviet Math. Dokl. 34, 373–376.
    • (1987) Doklady , vol.290
    • Gelfand, I.M.1    Goncharov, A.B.2
  • 18
    • 0010474509 scopus 로고
    • Spatial rotational alignment of identical particles given their projections: Theory and practice
    • Gelfand I. M. and Goncharov A. B. (1990), ‘Spatial rotational alignment of identical particles given their projections: Theory and practice’, Translation of Mathematical Monographs 81, 97–122.
    • (1990) Translation of Mathematical Monographs , vol.81 , pp. 97-122
    • Gelfand, I.M.1    Goncharov, A.B.2
  • 19
    • 0014905513 scopus 로고
    • Algebra reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography
    • Gordon R., Bender R. and Herman G. T. (1970), ‘Algebra reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography’, J. Theor. Biol. 29, 471–481.
    • (1970) J. Theor. Biol. , vol.29 , pp. 471-481
    • Gordon, R.1    Bender, R.2    Herman, G.T.3
  • 20
    • 0002018761 scopus 로고
    • Mathematical framework of cone-beam reconstruction via the first derivative of the Radon transform
    • (Herman G. T., Louis A. K., Natterer F., eds), Springer
    • Grangeat P. (1991), ‘Mathematical framework of cone-beam reconstruction via the first derivative of the Radon transform’, in Mathematical Methods in Tomography, Vol. 1497 of Lecture Notes in Mathematics (Herman G. T., Louis A. K. and Natterer F., eds), Springer, pp. 66–97.
    • (1991) Mathematical Methods in Tomography, Vol. 1497 of Lecture Notes in Mathematics , pp. 66-97
    • Grangeat, P.1
  • 21
    • 0025404969 scopus 로고
    • Bayesian reconstruction from emission tomography data using a modified EM algorithm
    • Green P. J. (1990), ‘Bayesian reconstruction from emission tomography data using a modified EM algorithm’, IEEE Trans. Med. Imag. 9, 84–93.
    • (1990) IEEE Trans. Med. Imag. , vol.9 , pp. 84-93
    • Green, P.J.1
  • 22
    • 0002164611 scopus 로고
    • The angles between the null spaces of X-rays
    • Hamaker C. and Solmon D. C. (1978), ‘The angles between the null spaces of X-rays’, J. Math. Anal. Appl. 62, 1–23.
    • (1978) J. Math. Anal. Appl. , vol.62 , pp. 1-23
    • Hamaker, C.1    Solmon, D.C.2
  • 23
    • 0019596565 scopus 로고
    • Circular harmonic image reconstruction
    • Hansen E. W. (1981), ‘Circular harmonic image reconstruction’, Applied Optics 20, 2266–2274.
    • (1981) Applied Optics , vol.20 , pp. 2266-2274
    • Hansen, E.W.1
  • 24
    • 0022766611 scopus 로고
    • A numerically stable circular harmonic reconstruction algorithm
    • Hawkins W. G. and Barrett H. H. (1986), ‘A numerically stable circular harmonic reconstruction algorithm’, SIAM J. Numer. Anal. 23, 873–890.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 873-890
    • Hawkins, W.G.1    Barrett, H.H.2
  • 26
    • 0027659444 scopus 로고
    • Algebraic reconstruction techniques can be made computationally efficient
    • Herman G. T. and Meyer L. (1993), ‘Algebraic reconstruction techniques can be made computationally efficient’, IEEE Trans. Med. Imag. 12, 600–609.
    • (1993) IEEE Trans. Med. Imag. , vol.12 , pp. 600-609
    • Herman, G.T.1    Meyer, L.2
  • 27
    • 0000203955 scopus 로고
    • Accelerated EM reconstruction using ordered subsets
    • Hudson H. M., Hutton B. F. and Larkin R. (1992), ‘Accelerated EM reconstruction using ordered subsets’, J. Nucl. Med. 33, 960–968.
    • (1992) J. Nucl. Med. , vol.33 , pp. 960-968
    • Hudson, H.M.1    Hutton, B.F.2    Larkin, R.3
  • 28
    • 0017558676 scopus 로고
    • The Shannon sampling theorem - its various extensions and applications: a tutorial review
    • Jerry A. J. (1977), ‘The Shannon sampling theorem - its various extensions and applications: a tutorial review’, Proc. IEEE 65, 1565–1596.
    • (1977) Proc. IEEE , vol.65 , pp. 1565-1596
    • Jerry, A.J.1
  • 31
    • 0001868550 scopus 로고
    • Computer assisted diffraction tomography
    • (Stark H., ed.), Academic Press
    • Kaveh M. and Soumekh M. (1987), ‘Computer assisted diffraction tomography’, in Image Recovery: Theory and Application (Stark H., ed.), Academic Press, pp. 369–413.
    • (1987) Image Recovery: Theory and Application , pp. 369-413
    • Kaveh, M.1    Soumekh, M.2
  • 32
    • 0001246255 scopus 로고
    • Resolution of reconstruction methods in computerized tomography
    • Kruse H. (1989), ‘Resolution of reconstruction methods in computerized tomography’, SIAM J. Sci. Statist. Comput. 10, 447–474.
    • (1989) SIAM J. Sci. Statist. Comput. , vol.10 , pp. 447-474
    • Kruse, H.1
  • 33
    • 0023421482 scopus 로고
    • A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography
    • Levitan E. and Herman G. T. (1987), ‘A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography’, IEEE Trans. Med. Imag. 6, 185–192.
    • (1987) IEEE Trans. Med. Imag. , vol.6 , pp. 185-192
    • Levitan, E.1    Herman, G.T.2
  • 34
    • 0026544838 scopus 로고
    • Alternatives to voxels for image representations in iterative reconstruction algorithms
    • Lewitt R. M. (1992), ‘Alternatives to voxels for image representations in iterative reconstruction algorithms’, Phys. Med. Biol. 37, 705–716.
    • (1992) Phys. Med. Biol. , vol.37 , pp. 705-716
    • Lewitt, R.M.1
  • 35
    • 0019148442 scopus 로고
    • Picture reconstruction from projections in restricted range
    • Louis A. K. (1980), ‘Picture reconstruction from projections in restricted range’, Math. Meth. Appl. Sci. 2, 109–220.
    • (1980) Math. Meth. Appl. Sci. , vol.2 , pp. 109-220
    • Louis, A.K.1
  • 36
    • 0011309772 scopus 로고    scopus 로고
    • Fully three-dimensional reconstruction in electron microscopy
    • (Borgers C. and Natterer F., eds), of IMA Volumes in Mathematics and its Applications, Springer
    • Marabini R., Herman G. T. and Carazo J. M. (1998), ‘Fully three-dimensional reconstruction in electron microscopy’, in Computational Radiology and Imaging: Therapy and Diagnostics (Borgers C. and Natterer F., eds), Vol. 110 of IMA Volumes in Mathematics and its Applications, Springer.
    • (1998) Computational Radiology and Imaging: Therapy and Diagnostics , vol.110
    • Marabini, R.1    Herman, G.T.2    Carazo, J.M.3
  • 37
    • 0001598883 scopus 로고
    • On two approaches to 3D reconstruction in NMR zeugmatography
    • (Herman G. T. and Natterer F., eds), Proceedings, Oberwolfach 1980, Springer
    • Marr R. B., Chen C. N. and Lauterbur P. C. (1981), ‘On two approaches to 3D reconstruction in NMR zeugmatography’, in Mathematical Aspects of Computerized Tomography (Herman G. T. and Natterer F., eds), Proceedings, Oberwolfach 1980, Springer, pp. 225–240.
    • (1981) Mathematical Aspects of Computerized Tomography , pp. 225-240
    • Marr, R.B.1    Chen, C.N.2    Lauterbur, P.C.3
  • 39
    • 0027574252 scopus 로고
    • Sampling in fan beam tomography
    • Natterer F. (1993), ‘Sampling in fan beam tomography’, SIAM J. Appl. Math. 53, 358–380.
    • (1993) SIAM J. Appl. Math. , vol.53 , pp. 358-380
    • Natterer, F.1
  • 41
    • 0004171666 scopus 로고    scopus 로고
    • Application of fast backprojection techniques for some inverse problems of integral geometry
    • Dissertation No. 499, Department of Mathematics, Linköping University, Linköping, Sweden
    • Nilsson S. (1997), ‘Application of fast backprojection techniques for some inverse problems of integral geometry’, Linköping Studies in Science and Technology, Dissertation No. 499, Department of Mathematics, Linköping University, Linköping, Sweden.
    • (1997) Linköping Studies in Science and Technology
    • Nilsson, S.1
  • 43
    • 0000337824 scopus 로고
    • Theory of three dimensional reconstruction, II: The recovery operator
    • Orlov S. S. (1976), ‘Theory of three dimensional reconstruction, II: The recovery operator’, Sov. Phys. Crystallogr. 20, 429–433.
    • (1976) Sov. Phys. Crystallogr. , vol.20 , pp. 429-433
    • Orlov, S.S.1
  • 44
    • 0022187595 scopus 로고
    • A fast sinc function gridding algorithm for Fourier inversion in computer tomography
    • O'Sullivan J. D. (1985), ‘A fast sinc function gridding algorithm for Fourier inversion in computer tomography’, IEEE Trans. Med. Imag. 4, 200–207.
    • (1985) IEEE Trans. Med. Imag. , vol.4 , pp. 200-207
    • O'Sullivan, J.D.1
  • 45
    • 0039579294 scopus 로고
    • Multiplicative interative methods in computed tomography
    • (Herman G. T., Louis A. K. and Natterer F., eds), Springer
    • De Pierro A. R. (1990), ‘Multiplicative interative methods in computed tomography’, in Mathematical Methods in Tomography (Herman G. T., Louis A. K. and Natterer F., eds), Springer, pp. 167–186.
    • (1990) Mathematical Methods in Tomography , pp. 167-186
    • De Pierro, A.R.1
  • 46
    • 0001169360 scopus 로고
    • Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten
    • Leipzig.
    • Radon J. (1917), ‘Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten’, Berichte Sächsische Akademie der Wissenschaften, Math.-Phys. Kl., 69, 262–267, Leipzig.
    • (1917) Berichte Sächsische Akademie der Wissenschaften, Math.-Phys. Kl. , vol.69 , pp. 262-267
    • Radon, J.1
  • 48
    • 0029378348 scopus 로고
    • The gridding method for image reconstruction bx Fourier transformation
    • Schomberg H. and Timmer J. (1995), ‘The gridding method for image reconstruction bx Fourier transformation’, IEEE Trans. Med. Imag. 14, 596–607.
    • (1995) IEEE Trans. Med. Imag. , vol.14 , pp. 596-607
    • Schomberg, H.1    Timmer, J.2
  • 49
    • 0016068330 scopus 로고
    • The Fourier reconstruction of a head section
    • Shepp L. A. and Logan B. F. (1974), ‘The Fourier reconstruction of a head section’, IEEE Trans. Trans. Nucl. Sci. NS-21, 21–43.
    • (1974) IEEE Trans. Trans. Nucl. Sci. , vol.NS-21 , pp. 21-43
    • Shepp, L.A.1    Logan, B.F.2
  • 50
    • 0020194763 scopus 로고
    • Maximum likelihood reconstruction for emission tomography
    • Shepp L. A. and Vardi Y. (1982), ‘Maximum likelihood reconstruction for emission tomography’, IEEE Trans. Med. Imag. 1, 113–122.
    • (1982) IEEE Trans. Med. Imag. , vol.1 , pp. 113-122
    • Shepp, L.A.1    Vardi, Y.2
  • 51
    • 0004091552 scopus 로고
    • ESNM: Ein rauschunterdrückendes EM-Verfahren für die Emissionstomographie
    • Dissertation, Fachbereich Mathematik, Universität Münster
    • Setzepfandt B. (1992), ‘ESNM: Ein rauschunterdrückendes EM-Verfahren für die Emissionstomographie’, Dissertation, Fachbereich Mathematik, Universität Münster.
    • (1992)
    • Setzepfandt, B.1
  • 52
    • 0344102022 scopus 로고
    • Use of collocation methods under inclusion of a priori information in acoustic pyrometry
    • Bergen, Norway
    • Sielschott H. and Derichs W. (1995), ‘Use of collocation methods under inclusion of a priori information in acoustic pyrometry’, Proc. European Concerted Action on Process Tomography, Bergen, Norway, pp. 110–117.
    • (1995) Proc. European Concerted Action on Process Tomography , pp. 110-117
    • Sielschott, H.1    Derichs, W.2
  • 53
    • 0002752852 scopus 로고
    • A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography
    • Silverman B. W., Jones M. C., Nychka D. W. and Wilson J. D. (1990), ‘A smoothed EM approach to indirect estimation problems, with particular reference to stereology and emission tomography’, J. R. Statist. Soc. B 52, 271–324.
    • (1990) J. R. Statist. Soc. B , vol.52 , pp. 271-324
    • Silverman, B.W.1    Jones, M.C.2    Nychka, D.W.3    Wilson, J.D.4
  • 54
    • 0020764170 scopus 로고
    • An inversion formula for cone-beam reconstruction
    • Tuy H. K. (1983), ‘An inversion formula for cone-beam reconstruction’, SIAM J. Appl. Math. 43, 546–552.
    • (1983) SIAM J. Appl. Math. , vol.43 , pp. 546-552
    • Tuy, H.K.1
  • 56
    • 85011447719 scopus 로고
    • Die Rekonstruktion von Orientierungen aus Projektionen
    • Diplomarbeit, Institut für Numerische und Instrumentelle Mathematik, Universität Münster.
    • Wuschke K. (1990), ‘Die Rekonstruktion von Orientierungen aus Projektionen’, Diplomarbeit, Institut für Numerische und Instrumentelle Mathematik, Universität Münster.
    • (1990)
    • Wuschke, K.1


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