메뉴 건너뛰기




Volumn 38, Issue 2, 2006, Pages 681-692

A range description for the planar circular Radon transform

Author keywords

Radon transform; Range description; Thermoacoustic tomography

Indexed keywords

RADON TRANSFORM; RANGE DESCRIPTION; THERMOACOUSTIC TOMOGRAPHY;

EID: 33947202591     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/050637492     Document Type: Article
Times cited : (59)

References (70)
  • 2
    • 0030213465 scopus 로고    scopus 로고
    • Injectivity sets for the Radon transform over circles and complete systems of radial functions
    • M. L. AGRANOVSKY AND E. T. QUINTO, Injectivity sets for the Radon transform over circles and complete systems of radial functions, J. Funct. Anal., 139 (1996), pp. 383-413.
    • (1996) J. Funct. Anal , vol.139 , pp. 383-413
    • AGRANOVSKY, M.L.1    QUINTO, E.T.2
  • 3
    • 0030457173 scopus 로고    scopus 로고
    • Range conditions for the exponential Radon transform
    • V. AGUILAR, L. EHRENPREIS, AND P. KUCHMENT, Range conditions for the exponential Radon transform, J. Anal. Math., 68 (1996), pp. 1-13.
    • (1996) J. Anal. Math , vol.68 , pp. 1-13
    • AGUILAR, V.1    EHRENPREIS, L.2    KUCHMENT, P.3
  • 4
    • 0010235835 scopus 로고
    • Range conditions for the multidimensional exponential X-ray transform
    • V. AGUILAR AND P. KUCHMENT, Range conditions for the multidimensional exponential X-ray transform, Inverse Problems, 11 (1995), pp. 977-982.
    • (1995) Inverse Problems , vol.11 , pp. 977-982
    • AGUILAR, V.1    KUCHMENT, P.2
  • 5
    • 17444386013 scopus 로고    scopus 로고
    • On the injectivity of the circular Radon transform arising in thermoacoustic tomography
    • G. AMBARTSOUMIAN AND P. KUCHMENT, On the injectivity of the circular Radon transform arising in thermoacoustic tomography, Inverse Problems, 21 (2005), pp. 473-485.
    • (2005) Inverse Problems , vol.21 , pp. 473-485
    • AMBARTSOUMIAN, G.1    KUCHMENT, P.2
  • 6
    • 0000422080 scopus 로고
    • On the determination of a function from spherical averages
    • L.-E. ANDERSSON, On the determination of a function from spherical averages, SIAM J. Math. Anal., 19 (1988), pp. 214-232.
    • (1988) SIAM J. Math. Anal , vol.19 , pp. 214-232
    • ANDERSSON, L.-E.1
  • 7
    • 0004167330 scopus 로고    scopus 로고
    • Encyclopedia Math. Appl. 71, Cambridge University Press, Cambridge, UK
    • G. E. ANDREWS, R. ASKEY, AND R. ROY, Special Functions, Encyclopedia Math. Appl. 71, Cambridge University Press, Cambridge, UK, 1999.
    • (1999) Special Functions
    • ANDREWS, G.E.1    ASKEY, R.2    ROY, R.3
  • 9
    • 0009984181 scopus 로고
    • The mathematics and physics of radiation dose planning
    • A. CORMACK AND E. T. QUINTO, The mathematics and physics of radiation dose planning, Contemp. Math., 113 (1990), pp. 41-55.
    • (1990) Contemp. Math , vol.113 , pp. 41-55
    • CORMACK, A.1    QUINTO, E.T.2
  • 10
    • 0003346454 scopus 로고
    • Methods of Mathematical Physics
    • Interscience, New York
    • R. COURANT AND D. HILBERT, Methods of Mathematical Physics, Volume II: Partial Differential Equations, Interscience, New York, 1962.
    • (1962) Partial Differential Equations , vol.2
    • COURANT, R.1    HILBERT, D.2
  • 12
    • 1942482497 scopus 로고    scopus 로고
    • Integral geometry on the family of semi-spheres
    • A. DENISJUK, Integral geometry on the family of semi-spheres, Fract. Calc. Appl. Anal., 2 (1999), pp. 31-46.
    • (1999) Fract. Calc. Appl. Anal , vol.2 , pp. 31-46
    • DENISJUK, A.1
  • 14
    • 0022045245 scopus 로고
    • Inversion of n-dimensional spherical averages
    • J. A. FAWCETT, Inversion of n-dimensional spherical averages, SIAM J. Appl. Math., 45 (1985), pp. 336-341.
    • (1985) SIAM J. Appl. Math , vol.45 , pp. 336-341
    • FAWCETT, J.A.1
  • 15
    • 33744526741 scopus 로고    scopus 로고
    • The range of the spherical mean value operator for functions supported in a ball
    • D. FINCH AND RAKESH, The range of the spherical mean value operator for functions supported in a ball, Inverse Problems, 22 (2006), pp. 923-938.
    • (2006) Inverse Problems , vol.22 , pp. 923-938
    • FINCH, D.1    RAKESH2
  • 16
    • 3042713885 scopus 로고    scopus 로고
    • Determining a function from its mean values over a family of spheres
    • D. FINCH, S. K. PATCH, AND RAKESH, Determining a function from its mean values over a family of spheres, SIAM J. Math. Anal., 35 (2004), pp. 1213-1240.
    • (2004) SIAM J. Math. Anal , vol.35 , pp. 1213-1240
    • FINCH, D.1    PATCH, S.K.2    RAKESH3
  • 17
    • 0003077448 scopus 로고
    • Integral geometry in affine and protective spaces
    • I. GELFAND, S. GINDIKIN, AND M. GRAEV, Integral geometry in affine and protective spaces, J. Sov. Math., 18 (1980), pp. 39-167.
    • (1980) J. Sov. Math , vol.18 , pp. 39-167
    • GELFAND, I.1    GINDIKIN, S.2    GRAEV, M.3
  • 20
    • 33947205283 scopus 로고    scopus 로고
    • S. GINDIKIN, Integral geometry on real quadrics, in Lie Groups and Lie Algebras: E. B. Dynkin's Seminar, Amer. Math. Soc. Transl. Ser. 2, 169, AMS, Providence, RI, 1995, pp. 23-31.
    • S. GINDIKIN, Integral geometry on real quadrics, in Lie Groups and Lie Algebras: E. B. Dynkin's Seminar, Amer. Math. Soc. Transl. Ser. 2, 169, AMS, Providence, RI, 1995, pp. 23-31.
  • 23
    • 0000965078 scopus 로고
    • Some problems of integral geometry and some related problems in microlocal analysis
    • V. GUILLEMIN AND S. STERENBERG, Some problems of integral geometry and some related problems in microlocal analysis, Amer. J. Math., 101 (1979), pp. 915-955.
    • (1979) Amer. J. Math , vol.101 , pp. 915-955
    • GUILLEMIN, V.1    STERENBERG, S.2
  • 24
    • 0346390664 scopus 로고
    • Single-photon emission computed tomography by inverting the attenuated Radon transform with least-squares collocation
    • U. HEIKE, Single-photon emission computed tomography by inverting the attenuated Radon transform with least-squares collocation, Inverse Problems, 2 (1986), pp. 307-330.
    • (1986) Inverse Problems , vol.2 , pp. 307-330
    • HEIKE, U.1
  • 26
    • 0011048318 scopus 로고
    • The identification problem for the constantly attenuated Radon transform
    • A. HERTLE, The identification problem for the constantly attenuated Radon transform, Math. Z., 197 (1988), pp. 13-19.
    • (1988) Math. Z , vol.197 , pp. 13-19
    • HERTLE, A.1
  • 29
    • 0028882213 scopus 로고
    • Photoacoustic ultrasound (PAUS) reconstruction tomography
    • R. A. KRUGER, P. LIU, Y. R. FANG, AND C. R. APPLEDORN, Photoacoustic ultrasound (PAUS) reconstruction tomography, Med. Phys., 22 (1995), pp. 1605-1609.
    • (1995) Med. Phys , vol.22 , pp. 1605-1609
    • KRUGER, R.A.1    LIU, P.2    FANG, Y.R.3    APPLEDORN, C.R.4
  • 30
    • 33947266181 scopus 로고
    • On positivity problems for the Radon transform and some related transforms
    • P. KUCHMENT, On positivity problems for the Radon transform and some related transforms, Contemp. Math., 140 (1993), pp. 87-95.
    • (1993) Contemp. Math , vol.140 , pp. 87-95
    • KUCHMENT, P.1
  • 31
    • 33947220564 scopus 로고    scopus 로고
    • P. KUCHMENT, Generalized transforms of Radon type and their applications, in The Radon Transform, Inverse Problems, and Tomography, G. Olafsson and E. T. Quinto, eds., Proc. Sympos. Appl. Math. 63, AMS, Providence, RI, 2006, pp. 67-91.
    • P. KUCHMENT, Generalized transforms of Radon type and their applications, in The Radon Transform, Inverse Problems, and Tomography, G. Olafsson and E. T. Quinto, eds., Proc. Sympos. Appl. Math. 63, AMS, Providence, RI, 2006, pp. 67-91.
  • 33
    • 0011270939 scopus 로고
    • Paley-Wiener theorem for exponential Radon transform
    • P. KUCHMENT AND S. LVIN, Paley-Wiener theorem for exponential Radon transform, Acta Appl. Math., 18 (1990), pp. 251-260.
    • (1990) Acta Appl. Math , vol.18 , pp. 251-260
    • KUCHMENT, P.1    LVIN, S.2
  • 34
    • 0011348563 scopus 로고
    • The range of the exponential Radon transform
    • P. KUCHMENT AND S. LVIN, The range of the exponential Radon transform, Soviet Math. Dokl., 42 (1991), pp. 183-184.
    • (1991) Soviet Math. Dokl , vol.42 , pp. 183-184
    • KUCHMENT, P.1    LVIN, S.2
  • 38
    • 38248999102 scopus 로고    scopus 로고
    • V. YA. LIN AND A. PINKUS, Fundamentality of ridge functions, J. Approx. Theory, 75 (1993), pp. 295-311.
    • V. YA. LIN AND A. PINKUS, Fundamentality of ridge functions, J. Approx. Theory, 75 (1993), pp. 295-311.
  • 39
    • 33947225363 scopus 로고    scopus 로고
    • V. YA. LIN AND A. PINKUS, Approximation of multivariable functions, in Advances in Computational Mathematics, H. P. Dikshit and C. A. Micchelli, eds., World Scientific, River Edge, NJ, 1994, pp. 1-9.
    • V. YA. LIN AND A. PINKUS, Approximation of multivariable functions, in Advances in Computational Mathematics, H. P. Dikshit and C. A. Micchelli, eds., World Scientific, River Edge, NJ, 1994, pp. 1-9.
  • 41
    • 34249736605 scopus 로고
    • Tomography, Impedance Imaging, and Integral Geometry, Lectures in Appl. Math. 30, AMS, Providence, RI
    • S. LVIN, Data correction and restoration in emission tomography, in Tomography, Impedance Imaging, and Integral Geometry, Lectures in Appl. Math. 30, AMS, Providence, RI, 1994, pp. 149-155.
    • (1994) Data correction and restoration in emission tomography , pp. 149-155
    • LVIN, S.1
  • 42
    • 0032872072 scopus 로고    scopus 로고
    • Attenuation correction in SPECT using consistency conditions for the exponential ray transform
    • C. MENNESIER, F. NOO, R. CLACKDOYLE, G. BAL, AND L. DESBAT, Attenuation correction in SPECT using consistency conditions for the exponential ray transform, Phys. Med. Biol., 44 (1999), pp. 2483-2510.
    • (1999) Phys. Med. Biol , vol.44 , pp. 2483-2510
    • MENNESIER, C.1    NOO, F.2    CLACKDOYLE, R.3    BAL, G.4    DESBAT, L.5
  • 43
    • 33947266726 scopus 로고
    • Exploiting the range of Radon transform in tomography
    • P. Deuflhard and E. Hairer, eds, Birkhäuser-Verlag, Basel
    • F. NATTERER, Exploiting the range of Radon transform in tomography, in Numerical Treatment of Inverse Problems in Differential and Integral Equations, P. Deuflhard and E. Hairer, eds., Birkhäuser-Verlag, Basel, 1983, pp. 290-303.
    • (1983) Numerical Treatment of Inverse Problems in Differential and Integral Equations , pp. 290-303
    • NATTERER, F.1
  • 45
    • 0034832061 scopus 로고    scopus 로고
    • Inversion of the attenuated Radon transform
    • F. NATTERER, Inversion of the attenuated Radon transform, Inverse Problems, 17 (2001), pp. 113-119.
    • (2001) Inverse Problems , vol.17 , pp. 113-119
    • NATTERER, F.1
  • 48
    • 0036470767 scopus 로고    scopus 로고
    • Synthetic aperture inversion
    • C. J. NOLAN AND M. CHENEY, Synthetic aperture inversion, Inverse Problems, 18 (2002), pp. 221-235.
    • (2002) Inverse Problems , vol.18 , pp. 221-235
    • NOLAN, C.J.1    CHENEY, M.2
  • 49
    • 0037036606 scopus 로고    scopus 로고
    • Inversion of the 3D exponential X-ray transform for a half equatorial band and other semi-circular geometries
    • F. NOO, R. CLACKDOYLE, AND J.-M. WAGNER, Inversion of the 3D exponential X-ray transform for a half equatorial band and other semi-circular geometries, Phys. Med. Biol., 47 (2002), pp. 2727-35.
    • (2002) Phys. Med. Biol , vol.47 , pp. 2727-2735
    • NOO, F.1    CLACKDOYLE, R.2    WAGNER, J.-M.3
  • 50
    • 0035473378 scopus 로고    scopus 로고
    • Image reconstruction in 2D SPECT with 180° acquisition
    • F. NOO AND J.-M. WAGNER, Image reconstruction in 2D SPECT with 180° acquisition, Inverse Problems, 17 (2001), pp. 1357-1371.
    • (2001) Inverse Problems , vol.17 , pp. 1357-1371
    • NOO, F.1    WAGNER, J.-M.2
  • 51
    • 0019002759 scopus 로고
    • Reconstruction of a two-dimensional reflecting medium over a circular domain: Exact solution
    • S. J. NORTON, Reconstruction of a two-dimensional reflecting medium over a circular domain: Exact solution, J. Acoust. Soc. Amer., 67 (1980), pp. 1266-1273.
    • (1980) J. Acoust. Soc. Amer , vol.67 , pp. 1266-1273
    • NORTON, S.J.1
  • 52
    • 0019394034 scopus 로고
    • Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solutions for plane, cylindrical, and spherical apertures
    • S. J. NORTON AND M. LINZER, Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solutions for plane, cylindrical, and spherical apertures, IEEE Trans, Biomed. Engrg., 28 (1981), pp. 200-202.
    • (1981) IEEE Trans, Biomed. Engrg , vol.28 , pp. 200-202
    • NORTON, S.J.1    LINZER, M.2
  • 53
    • 0036609422 scopus 로고    scopus 로고
    • On the range characterization for the two-dimensional attenuated X-ray transform
    • R. NOVIKOV, On the range characterization for the two-dimensional attenuated X-ray transform, Inverse Problems, 18 (2002), pp. 677-700.
    • (2002) Inverse Problems , vol.18 , pp. 677-700
    • NOVIKOV, R.1
  • 54
    • 0012370548 scopus 로고    scopus 로고
    • Extension of separately analytic functions and applications to range characterization of the exponential Radon transform, in Complex Analysis and Applications (Warsaw, 1997)
    • O. OKTEM, Extension of separately analytic functions and applications to range characterization of the exponential Radon transform, in Complex Analysis and Applications (Warsaw, 1997), Ann. Polon. Math., 70 (1998), pp. 195-213.
    • (1998) Ann. Polon. Math , vol.70 , pp. 195-213
    • OKTEM, O.1
  • 55
    • 23044519030 scopus 로고    scopus 로고
    • Reconstruction from limited data of arc means
    • V. P. PALAMODOV, Reconstruction from limited data of arc means, J. Fourier Anal. Appl., 6 (2000), pp. 25-42.
    • (2000) J. Fourier Anal. Appl , vol.6 , pp. 25-42
    • PALAMODOV, V.P.1
  • 56
    • 3042781845 scopus 로고    scopus 로고
    • Thermoacoustic tomography - consistency conditions and the partial scan problem
    • S. K. PATCH, Thermoacoustic tomography - consistency conditions and the partial scan problem, Phys. Med. Biol., 49 (2004), pp. 1-11.
    • (2004) Phys. Med. Biol , vol.49 , pp. 1-11
    • PATCH, S.K.1
  • 57
    • 33947193178 scopus 로고
    • Correction of emission tomography data. Effects of detector displacement and nonconstant sensitivity
    • I. PONOMAREV, Correction of emission tomography data. Effects of detector displacement and nonconstant sensitivity, Inverse Problems, 10 (1995), pp. 1-8.
    • (1995) Inverse Problems , vol.10 , pp. 1-8
    • PONOMAREV, I.1
  • 58
    • 84968521990 scopus 로고
    • The dependence of the generalized Radon transform on defining measures
    • E. T. QUINTO, The dependence of the generalized Radon transform on defining measures, Trans. Amer. Math. Soc., 257 (1980), pp. 331-346.
    • (1980) Trans. Amer. Math. Soc , vol.257 , pp. 331-346
    • QUINTO, E.T.1
  • 59
    • 0020707822 scopus 로고
    • The invertibility of rotation invariant Radon transforms
    • E. T. QUINTO, The invertibility of rotation invariant Radon transforms, J. Math. Anal. Appl., 91 (1983), pp. 510-522.
    • (1983) J. Math. Anal. Appl , vol.91 , pp. 510-522
    • QUINTO, E.T.1
  • 60
    • 0013479909 scopus 로고
    • Null spaces and ranges for the classical and spherical Radon transforms
    • E. T. QUINTO, Null spaces and ranges for the classical and spherical Radon transforms, J. Math. Anal. Appl., 90 (1982), pp. 408-420.
    • (1982) J. Math. Anal. Appl , vol.90 , pp. 408-420
    • QUINTO, E.T.1
  • 64
    • 33947235319 scopus 로고
    • Two inverse problems for the exponential Radon transform
    • P. S. Sabatier, ed, Springer-Verlag, Berlin
    • D. SOLMON, Two inverse problems for the exponential Radon transform, in Inverse Problems in Action, P. S. Sabatier, ed., Springer-Verlag, Berlin, 1990, pp. 46-53.
    • (1990) Inverse Problems in Action , pp. 46-53
    • SOLMON, D.1
  • 65
    • 84988183251 scopus 로고
    • The identification problem for the exponential Radon transform
    • D. SOLMON, The identification problem for the exponential Radon transform, Math. Methods Appl. Sci., 18 (1995), pp. 687-695.
    • (1995) Math. Methods Appl. Sci , vol.18 , pp. 687-695
    • SOLMON, D.1
  • 66
    • 0001197863 scopus 로고
    • The exponential Radon transform
    • O. TRETIAK AND C. METZ, The exponential Radon transform, SIAM J. Appl. Math., 39 (1980), pp. 341-354.
    • (1980) SIAM J. Appl. Math , vol.39 , pp. 341-354
    • TRETIAK, O.1    METZ, C.2
  • 67
    • 0036628475 scopus 로고    scopus 로고
    • Time-domain reconstruction for thermoacoustic tomography in a spherical geometry
    • M. XU AND L.-H. V. WANG, Time-domain reconstruction for thermoacoustic tomography in a spherical geometry, IEEE Trans. Med. Imag., 21 (2002), pp. 814-822.
    • (2002) IEEE Trans. Med. Imag , vol.21 , pp. 814-822
    • XU, M.1    WANG, L.-H.V.2
  • 68
    • 0036628476 scopus 로고    scopus 로고
    • Exact frequency-domain reconstruction for thermoacoustic tomography I: Planar geometry
    • Y. XU, D. FENG, AND L.-H. V. WANG, Exact frequency-domain reconstruction for thermoacoustic tomography I: Planar geometry, IEEE Trans. Med. Imag., 21 (2002), pp. 823-828.
    • (2002) IEEE Trans. Med. Imag , vol.21 , pp. 823-828
    • XU, Y.1    FENG, D.2    WANG, L.-H.V.3
  • 69
    • 0036628477 scopus 로고    scopus 로고
    • Exact frequency-domain reconstruction for thermoacoustic tomography II: Cylindrical geometry
    • Y. XU, M. XU, AND L.-H. V. WANG, Exact frequency-domain reconstruction for thermoacoustic tomography II: Cylindrical geometry, IEEE Trans. Med. Imag., 21 (2002), pp. 829-833.
    • (2002) IEEE Trans. Med. Imag , vol.21 , pp. 829-833
    • XU, Y.1    XU, M.2    WANG, L.-H.V.3
  • 70
    • 1942516847 scopus 로고    scopus 로고
    • Reconstructions in limited view thermoacoustic tomography
    • Y. XU, L. WANG, G. AMBARTSOUMIAN, AND P. KUCHMENT, Reconstructions in limited view thermoacoustic tomography, Med. Phys., 31 (2004), pp. 724-733.
    • (2004) Med. Phys , vol.31 , pp. 724-733
    • XU, Y.1    WANG, L.2    AMBARTSOUMIAN, G.3    KUCHMENT, P.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.