메뉴 건너뛰기




Volumn 111, Issue 1, 2010, Pages 245-252

A stable numerical inversion of Abel's integral equation using almost Bernstein operational matrix

Author keywords

Abel inversion; Almost Bernstein operational matrix; Noise resistance

Indexed keywords

3D IMAGE RECONSTRUCTION; ABEL INVERSION; ALGEBRAIC EQUATIONS; ALMOST BERNSTEIN OPERATIONAL MATRIX; BERNSTEIN POLYNOMIAL; CONE-BEAM PROJECTION; INTENSITY DATA; INTENSITY PROFILES; LINE-OF-SIGHT; MATHEMATICAL SCIENCE; MATRIX P; NOISE RESISTANCE; NUMERICAL INVERSION; OPERATIONAL MATRICES; OPERATIONAL MATRIX OF INTEGRATION; ORTHONORMAL; RADIAL SYMMETRYS; RANDOM NOISE; STABLE ALGORITHMS; STABLE NUMERICAL SOLUTIONS;

EID: 70349838483     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2009.07.007     Document Type: Article
Times cited : (38)

References (41)
  • 1
    • 84941377590 scopus 로고
    • Resolution d'un probleme de mechanique
    • Abel N.H. Resolution d'un probleme de mechanique. J Reine Angew Math 1 (1826) 153-157
    • (1826) J Reine Angew Math , vol.1 , pp. 153-157
    • Abel, N.H.1
  • 3
    • 0016644563 scopus 로고
    • Abel type integral equations in stereology I. General discussion
    • Jaeman A.J., and Anderssen R.S. Abel type integral equations in stereology I. General discussion. J Microsc 105 (1975) 121-133
    • (1975) J Microsc , vol.105 , pp. 121-133
    • Jaeman, A.J.1    Anderssen, R.S.2
  • 4
    • 65549098588 scopus 로고
    • Evidence on the interior of the earth derived from seismic sources
    • Gutenberg B. (Ed), Dover, New York
    • Macelwane J.B. Evidence on the interior of the earth derived from seismic sources. In: Gutenberg B. (Ed). Internal constitution of the earth (1951), Dover, New York 227-304
    • (1951) Internal constitution of the earth , pp. 227-304
    • Macelwane, J.B.1
  • 5
    • 0036060873 scopus 로고    scopus 로고
    • Abel transform inversion of radio occultation measurements made with a receiver inside the Earth's atmosphere
    • Healy S.B., Haase J., and Lesne O. Abel transform inversion of radio occultation measurements made with a receiver inside the Earth's atmosphere. Ann Geophys 20 (2002) 1253-1256
    • (2002) Ann Geophys , vol.20 , pp. 1253-1256
    • Healy, S.B.1    Haase, J.2    Lesne, O.3
  • 6
    • 0000484921 scopus 로고
    • Inversion of fan-beam scans in radio astronomy
    • Bracewell R.N., and Riddle A.C. Inversion of fan-beam scans in radio astronomy. Astrophys J 150 (1967) 427-434
    • (1967) Astrophys J , vol.150 , pp. 427-434
    • Bracewell, R.N.1    Riddle, A.C.2
  • 7
    • 0021513292 scopus 로고
    • Tomographic inversion of satellite photometry
    • Solomon S.C., Hays P.B., and Abreu V.J. Tomographic inversion of satellite photometry. Appl Opt 23 (1984) 3409-3414
    • (1984) Appl Opt , vol.23 , pp. 3409-3414
    • Solomon, S.C.1    Hays, P.B.2    Abreu, V.J.3
  • 8
    • 0008486914 scopus 로고
    • Applications of integral equations of the first kind in experiment physics
    • Kosarev E.L. Applications of integral equations of the first kind in experiment physics. Comput Phys Commun 20 (1980) 69-75
    • (1980) Comput Phys Commun , vol.20 , pp. 69-75
    • Kosarev, E.L.1
  • 9
    • 0001302614 scopus 로고
    • Inversion of molecular scattering data
    • Buck U. Inversion of molecular scattering data. Rev Mod Phys 46 (1974) 369-389
    • (1974) Rev Mod Phys , vol.46 , pp. 369-389
    • Buck, U.1
  • 10
    • 0000436489 scopus 로고
    • An inverse method for the processing of synthetic aperture radar data
    • Hellsten H., and Andersson L.E. An inverse method for the processing of synthetic aperture radar data. Inverse Probl 3 (1987) 111-124
    • (1987) Inverse Probl , vol.3 , pp. 111-124
    • Hellsten, H.1    Andersson, L.E.2
  • 11
    • 65549084215 scopus 로고
    • Non destructive testing of optical-fiber performs
    • Anderssen R.S., and Calligaro R.B. Non destructive testing of optical-fiber performs. J Aust Math Soc (Ser B) 23 (1981) 127-135
    • (1981) J Aust Math Soc (Ser B) , vol.23 , pp. 127-135
    • Anderssen, R.S.1    Calligaro, R.B.2
  • 12
    • 0020269619 scopus 로고
    • Index profile determination of single-mode fiber by the phase contrast method: a proposed technique
    • Taketura K. Index profile determination of single-mode fiber by the phase contrast method: a proposed technique. Appl Opt 21 (1982) 4260-4263
    • (1982) Appl Opt , vol.21 , pp. 4260-4263
    • Taketura, K.1
  • 13
    • 0022072126 scopus 로고
    • How accurately can one reconstruct an index profile from transverse measurement data
    • Glantschnig W.J. How accurately can one reconstruct an index profile from transverse measurement data. IEEE J Lightwave Technol LT-3 (1985) 678-683
    • (1985) IEEE J Lightwave Technol , vol.LT-3 , pp. 678-683
    • Glantschnig, W.J.1
  • 14
    • 0019698726 scopus 로고
    • Measurements of temperature distribution of flames by moiré dflectometry
    • Keren E., Bar-Ziv E., Glatt I., and Kafri O. Measurements of temperature distribution of flames by moiré dflectometry. Appl Opt 20 (1981) 4263-4266
    • (1981) Appl Opt , vol.20 , pp. 4263-4266
    • Keren, E.1    Bar-Ziv, E.2    Glatt, I.3    Kafri, O.4
  • 15
    • 0020707634 scopus 로고
    • The determination of electron density profiles from refraction measurements obtained using holographic interferometry
    • Tallents C.J., Burgess M.D.J., and Luther-Davies B. The determination of electron density profiles from refraction measurements obtained using holographic interferometry. Opt Commun 4 (1983) 384-387
    • (1983) Opt Commun , vol.4 , pp. 384-387
    • Tallents, C.J.1    Burgess, M.D.J.2    Luther-Davies, B.3
  • 16
    • 0000613804 scopus 로고
    • Inversion of Abel's integral equation application to plasma spectroscopy
    • Fleurier C., and Chapelle J. Inversion of Abel's integral equation application to plasma spectroscopy. Comput Phys Commun 7 (1974) 200-206
    • (1974) Comput Phys Commun , vol.7 , pp. 200-206
    • Fleurier, C.1    Chapelle, J.2
  • 17
    • 0036497796 scopus 로고    scopus 로고
    • The realization of Abel's inversion in the case of discharge with undetermined radius
    • Ignjatovic Lj.M., and Mihajlov A.A. The realization of Abel's inversion in the case of discharge with undetermined radius. J Quant Spectrosc Radiat Transfer 72 (2002) 677-689
    • (2002) J Quant Spectrosc Radiat Transfer , vol.72 , pp. 677-689
    • Ignjatovic, Lj.M.1    Mihajlov, A.A.2
  • 20
    • 0023091799 scopus 로고
    • Mass fraction profiling based on X-ray tomography and its application to characterising porous silica boules
    • Glantschnig W.J., and Holliday A. Mass fraction profiling based on X-ray tomography and its application to characterising porous silica boules. Appl Opt 26 (1987) 983-989
    • (1987) Appl Opt , vol.26 , pp. 983-989
    • Glantschnig, W.J.1    Holliday, A.2
  • 21
    • 0001069532 scopus 로고
    • Representation of a function by its line integrals with some radiological applications
    • Cormack A.M. Representation of a function by its line integrals with some radiological applications. J Appl Phys 34 (1963) 2722-2727
    • (1963) J Appl Phys , vol.34 , pp. 2722-2727
    • Cormack, A.M.1
  • 22
    • 12544260746 scopus 로고
    • Representation of a function by its line integrals with some radiological applications
    • Cormack A.M. Representation of a function by its line integrals with some radiological applications. J Appl Phys 35 (1964) 2908-2913
    • (1964) J Appl Phys , vol.35 , pp. 2908-2913
    • Cormack, A.M.1
  • 23
    • 0025383926 scopus 로고
    • Inversion of Abel's integral equation and its application to NDT by X-ray radiography
    • Deutsch M., Notea A., and Pal D. Inversion of Abel's integral equation and its application to NDT by X-ray radiography. NDT Int 23 1 (1990)
    • (1990) NDT Int , vol.23 , Issue.1
    • Deutsch, M.1    Notea, A.2    Pal, D.3
  • 24
    • 0004056077 scopus 로고
    • McGraw-Hill Book Company, New York
    • Griem H.R. Plasma spectroscopy (1963), McGraw-Hill Book Company, New York
    • (1963) Plasma spectroscopy
    • Griem, H.R.1
  • 26
    • 0001249102 scopus 로고
    • Inversion of Abel's integral equation by means of orthogonal polynomials
    • Minerbo G.N., and Levy M.E. Inversion of Abel's integral equation by means of orthogonal polynomials. SIAM J Numer Anal 6 (1969) 598-616
    • (1969) SIAM J Numer Anal , vol.6 , pp. 598-616
    • Minerbo, G.N.1    Levy, M.E.2
  • 27
    • 0041874261 scopus 로고
    • Derivative-free inversion of Abel's integral equation
    • Deutsch M., and Beniaminy I. Derivative-free inversion of Abel's integral equation. Appl Phys Lett 41 (1982) 27-28
    • (1982) Appl Phys Lett , vol.41 , pp. 27-28
    • Deutsch, M.1    Beniaminy, I.2
  • 28
    • 84975576348 scopus 로고
    • Application of the Abel integral equation to spectroscopic data
    • Cremers C.J., and Birkebak R.C. Application of the Abel integral equation to spectroscopic data. Appl Opt 5 (1966) 1057-1064
    • (1966) Appl Opt , vol.5 , pp. 1057-1064
    • Cremers, C.J.1    Birkebak, R.C.2
  • 29
    • 0001190888 scopus 로고
    • Stable procedures for the inversion of Abel's equation
    • Anderssen R.S. Stable procedures for the inversion of Abel's equation. J Inst Math Appl 17 (1976) 329-342
    • (1976) J Inst Math Appl , vol.17 , pp. 329-342
    • Anderssen, R.S.1
  • 30
    • 0041373496 scopus 로고
    • Error attenuation in Abel inversion
    • Lanquart J.P. Error attenuation in Abel inversion. J Comput Phys 47 (1982) 434-443
    • (1982) J Comput Phys , vol.47 , pp. 434-443
    • Lanquart, J.P.1
  • 31
    • 33746258449 scopus 로고
    • Computation of rough solutions of Abel integral equation
    • Engel H.W., and Groetsch C.W. (Eds), Academic Press, New York
    • Grenflo R. Computation of rough solutions of Abel integral equation. In: Engel H.W., and Groetsch C.W. (Eds). Inverse III-posed problems (1987), Academic Press, New York 195-210
    • (1987) Inverse III-posed problems , pp. 195-210
    • Grenflo, R.1
  • 32
    • 84985743574 scopus 로고
    • Inversion of the Abel integral equation by use of simple interpolation formulas
    • Sato M. Inversion of the Abel integral equation by use of simple interpolation formulas. Contrib Plasma Phys 25 (1985) 573-577
    • (1985) Contrib Plasma Phys , vol.25 , pp. 573-577
    • Sato, M.1
  • 33
    • 36749111218 scopus 로고
    • Abel inversion with a simple analytic representation for experimental data
    • Deutsch M. Abel inversion with a simple analytic representation for experimental data. Appl Phys Lett 42 (1983) 237-239
    • (1983) Appl Phys Lett , vol.42 , pp. 237-239
    • Deutsch, M.1
  • 34
    • 65549090973 scopus 로고    scopus 로고
    • New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials
    • Singh V.K., Pandey R.K., and Singh O.P. New stable numerical solution of singular integral equations of Abel type by using normalized Bernstein polynomials. Appl Math Sci 3 5 (2009) 241-255
    • (2009) Appl Math Sci , vol.3 , Issue.5 , pp. 241-255
    • Singh, V.K.1    Pandey, R.K.2    Singh, O.P.3
  • 35
    • 5844398947 scopus 로고
    • Abel: stable high accuracy program for the inversion of Abel's integral equation
    • Beniaminy I., and Deutsch M. Abel: stable high accuracy program for the inversion of Abel's integral equation. Comput Phys Commun 27 (1982) 415-422
    • (1982) Comput Phys Commun , vol.27 , pp. 415-422
    • Beniaminy, I.1    Deutsch, M.2
  • 36
    • 44049118776 scopus 로고
    • New stable numerical inversion of Abel's integral equation
    • Murio D.A., Hinestroza D.G., and Mejia C.E. New stable numerical inversion of Abel's integral equation. Comput Math Appl 23 11 (1992) 3-11
    • (1992) Comput Math Appl , vol.23 , Issue.11 , pp. 3-11
    • Murio, D.A.1    Hinestroza, D.G.2    Mejia, C.E.3
  • 37
    • 65549100456 scopus 로고    scopus 로고
    • Use of Bernstein polynomials in numerical solutions of Volterra integral equations
    • Bhattacharya S., and Mandal B.N. Use of Bernstein polynomials in numerical solutions of Volterra integral equations. Appl Math Sci 2 36 (2008) 1773-1787
    • (2008) Appl Math Sci , vol.2 , Issue.36 , pp. 1773-1787
    • Bhattacharya, S.1    Mandal, B.N.2
  • 38
    • 43249103402 scopus 로고    scopus 로고
    • Abel inversion using Legendre polynomials approximations
    • Ma S., Gao H., Wu L., and Zhang G. Abel inversion using Legendre polynomials approximations. J Quant Spectrosc Radiat Transfer 109 (2008) 1745-1757
    • (2008) J Quant Spectrosc Radiat Transfer , vol.109 , pp. 1745-1757
    • Ma, S.1    Gao, H.2    Wu, L.3    Zhang, G.4
  • 40
    • 70349835970 scopus 로고
    • PhD thesis, University of Minnesota;
    • C.J. Cremers, PhD thesis, University of Minnesota; 1964.
    • (1964)
    • Cremers, C.J.1
  • 41
    • 48049097506 scopus 로고    scopus 로고
    • Approximate solution of Abel integral equation
    • Huang Li., Huang Y., and Lian X. Approximate solution of Abel integral equation. Comput Math Appl 56 (2008) 1748-1757
    • (2008) Comput Math Appl , vol.56 , pp. 1748-1757
    • Huang, Li.1    Huang, Y.2    Lian, X.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.