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Volumn 34, Issue 8, 2013, Pages 819-844

Approximation by nonlinear multivariate sampling kantorovich type operators and applications to image processing

Author keywords

Exponential spaces; Image processing; Irregular sampling; L log L spaces; Modular convergence; Orlicz spaces; Sampling Kantorovich operators

Indexed keywords

CONVERGENCE THEOREM; EXPONENTIAL SPACES; GRAPHICAL REPRESENTATIONS; IMAGE PROCESSING APPLICATIONS; IRREGULAR SAMPLING; MODULAR CONVERGENCE; ORLICZ SPACES; UNIFORMLY CONTINUOUS;

EID: 84880406518     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630563.2013.767833     Document Type: Article
Times cited : (69)

References (38)
  • 2
    • 84874614569 scopus 로고    scopus 로고
    • Modular approximation by sequences of nonlinear integral operators in Musielak-Orlicz spaces
    • C. Bardaro. and, I. Mantellini. (1998). Modular approximation by sequences of nonlinear integral operators in Musielak-Orlicz spaces. Atti Sem. Mat. Fis. Univ. 46 (S): 403-425.
    • (1998) Atti Sem. Mat. Fis. Univ. , vol.46 , Issue.S , pp. 403-425
    • Bardaro, C.1    Mantellini, I.2
  • 4
    • 2442676148 scopus 로고    scopus 로고
    • Uniform convergence and rate of approximation for a nonlinear version of the generalized sampling operator
    • C. Bardaro. and, G. Vinti. (1998). Uniform convergence and rate of approximation for a nonlinear version of the generalized sampling operator. Result Math. 34: 224-240.
    • (1998) Result Math. , vol.34 , pp. 224-240
    • Bardaro, C.1    Vinti, G.2
  • 5
    • 27844444162 scopus 로고    scopus 로고
    • An abstract approach to sampling type operators inspired by the work of P.L. Butzer - Part II - Nonlinear operators
    • C. Bardaro. and, G. Vinti. (2004). An abstract approach to sampling type operators inspired by the work of P.L. Butzer-Part II-Nonlinear operators. Sampling Theory in Signal and Image Processing 3 (1): 29-44.
    • (2004) Sampling Theory in Signal and Image Processing , vol.3 , Issue.1 , pp. 29-44
    • Bardaro, C.1    Vinti, G.2
  • 6
    • 0004252330 scopus 로고
    • On lorentz-zygmund spaces
    • Państwowe Wydawnictwo Naukowe, Warszawa
    • C. Bennet. and, K. Rudnick. (1980). On Lorentz-Zygmund Spaces. Dissertationes Math. (Rozprawy Mat.), Vol. 175. Państwowe Wydawnictwo Naukowe, Warszawa.
    • (1980) Dissertationes Math. (Rozprawy Mat.) , vol.175
    • Bennet, C.1    Rudnick, K.2
  • 8
    • 0001114755 scopus 로고
    • A survey of the Whittaker-Shannon sampling theorem and some of its extensions
    • P. L. Butzer. (1983). A survey of the Whittaker-Shannon sampling theorem and some of its extensions. J. Math. Res. Exposition 3: 185-212.
    • (1983) J. Math. Res. Exposition , vol.3 , pp. 185-212
    • Butzer, P.L.1
  • 9
    • 0022699123 scopus 로고
    • The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines
    • P. L. Butzer., W. Engels., S. Ries., and, R. L. Stens. (1986). The Shannon sampling series and the reconstruction of signals in terms of linear, quadratic and cubic splines. SIAM J. Appl. Math. 46: 299-323.
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 299-323
    • Butzer, P.L.1    Engels, W.2    Ries, S.3    Stens, R.L.4
  • 10
    • 0010923391 scopus 로고
    • Generalized sampling approximation of multivariate signals: Theory and applications
    • P. L. Butzer., A. Fisher., and, R. L. Stens. (1990). Generalized sampling approximation of multivariate signals: theory and applications. Note di Matematica 10 (S1): 173-191.
    • (1990) Note di Matematica , vol.10 , Issue.S1 , pp. 173-191
    • Butzer, P.L.1    Fisher, A.2    Stens, R.L.3
  • 11
    • 0024664737 scopus 로고
    • Reconstruction of bounded signal from pseudoperiodic, irregularly spaced samples
    • P. L. Butzer. and, G. Hinsen. (1989). Reconstruction of bounded signal from pseudoperiodic, irregularly spaced samples. Signal Processing 17: 1-17.
    • (1989) Signal Processing , vol.17 , pp. 1-17
    • Butzer, P.L.1    Hinsen, G.2
  • 13
    • 38249033946 scopus 로고
    • Approximation of continuous and discountinuous functions by generalized sampling series
    • P. L. Butzer., S. Ries., and, R. L. Stens. (1987). Approximation of continuous and discountinuous functions by generalized sampling series. J. Approx. Theory 50: 25-39.
    • (1987) J. Approx. Theory , vol.50 , pp. 25-39
    • Butzer, P.L.1    Ries, S.2    Stens, R.L.3
  • 15
    • 0026838009 scopus 로고
    • Sampling theory for not necessarily band-limited functions: A historical overview
    • P. L. Butzer. and, R. L. Stens. (1992). Sampling theory for not necessarily band-limited functions: a historical overview. SIAM Review 34 (1): 40-53.
    • (1992) SIAM Review , vol.34 , Issue.1 , pp. 40-53
    • Butzer, P.L.1    Stens, R.L.2
  • 16
    • 27844557036 scopus 로고
    • Linear prediction by samples from the past
    • (R. J. Marks, II, ed.). Springer-Verlag, New York
    • P. L. Butzer. and, R. L. Stens. (1993). Linear prediction by samples from the past. In: Advanced Topics in Shannon Sampling and Interpolation Theory (R. J. Marks, II., ed.). Springer-Verlag, New York, pp. 157-177.
    • (1993) Advanced Topics in Shannon Sampling and Interpolation Theory , pp. 157-177
    • Butzer, P.L.1    Stens, R.L.2
  • 17
    • 84874596412 scopus 로고    scopus 로고
    • Approximation by multivariate generalized sampling Kantorovich operators in the setting of Orlicz spaces
    • D. Costarelli. and, G. Vinti. (2011). Approximation by multivariate generalized sampling Kantorovich operators in the setting of Orlicz spaces. Bollettino UMI 9 (4): 445-468.
    • (2011) Bollettino UMI , vol.9 , Issue.4 , pp. 445-468
    • Costarelli, D.1    Vinti, G.2
  • 18
    • 0002843453 scopus 로고
    • Fourier analysis and the sampling theorem
    • M. M. Dodson. and, A. M. Silva. (1985). Fourier analysis and the sampling theorem. Proc. Ir. Acad. 86A: 81-108.
    • (1985) Proc. Ir. Acad. , vol.86 A , pp. 81-108
    • Dodson, M.M.1    Silva, A.M.2
  • 19
    • 0001204748 scopus 로고
    • Two limiting cases of Sobolev embeddings
    • D. E. Edmunds. and, M. Krbec. (1995). Two limiting cases of Sobolev embeddings. Houston J. Math. 21 (1): 119-128.
    • (1995) Houston J. Math. , vol.21 , Issue.1 , pp. 119-128
    • Edmunds, D.E.1    Krbec, M.2
  • 20
    • 0142087806 scopus 로고    scopus 로고
    • A sharp form of an embedding into exponential and double exponential spaces
    • S. Hencl. (2003). A sharp form of an embedding into exponential and double exponential spaces. J. Funct. Anal. 204 (1): 196-227.
    • (2003) J. Funct. Anal. , vol.204 , Issue.1 , pp. 196-227
    • Hencl, S.1
  • 21
    • 84968515233 scopus 로고
    • Five short stories about the cardinal series
    • J. R. Higgins. (1985). Five short stories about the cardinal series. Bull. Amer. Math. Soc. 12: 45-89.
    • (1985) Bull. Amer. Math. Soc. , vol.12 , pp. 45-89
    • Higgins, J.R.1
  • 24
    • 0017558676 scopus 로고
    • The Shannon sampling-its various extensions and applications: A tutorial review
    • A. J. Jerry. (1977). The Shannon sampling-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
  • 25
    • 0141871125 scopus 로고
    • Modular function spaces
    • Marcel Dekker, New York
    • W. M. Kozlowski. (1988). Modular Function Spaces. Pure Applied Mathematics, Marcel Dekker, New York.
    • (1988) Pure Applied Mathematics
    • Kozlowski, W.M.1
  • 28
    • 27844556091 scopus 로고    scopus 로고
    • Approximation results for nonlinear integral operators in modular spaces and applications
    • I. Mantellini. and, G. Vinti. (2003). Approximation results for nonlinear integral operators in modular spaces and applications. Ann. Polon. Math. 81 (1): 55-71.
    • (2003) Ann. Polon. Math. , vol.81 , Issue.1 , pp. 55-71
    • Mantellini, I.1    Vinti, G.2
  • 29
    • 0003311060 scopus 로고
    • Orlicz spaces and modular spaces
    • Springer-Verlag, Berlin
    • J. Musielak. (1983). Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, Berlin.
    • (1983) Lecture Notes in Mathematics , vol.1034
    • Musielak, J.1
  • 30
  • 33
    • 0010797227 scopus 로고
    • Approximation by generalized sampling series
    • (Bl. Sendov, P. Petrushev, R. Maleev, and S. Tashev, eds.). Bulgarian Academy of Sciences, Sofia
    • S. Ries. and, R. L. Stens. (1984). Approximation by generalized sampling series. In: Constructive Theory of Functions, Proc. Conf. Varna, Bulgaria. (Bl. Sendov., P. Petrushev., R. Maleev., and S. Tashev., eds.). Bulgarian Academy of Sciences, Sofia, pp. 746-756.
    • (1984) Constructive Theory of Functions, Proc. Conf. Varna, Bulgaria , pp. 746-756
    • Ries, S.1    Stens, R.L.2
  • 34
    • 84911837213 scopus 로고
    • Communication in the presence of noise
    • C. E. Shannon. (1949). Communication in the presence of noise. Proc. IRE 37: 10-21.
    • (1949) Proc. IRE , vol.37 , pp. 10-21
    • Shannon, C.E.1
  • 35
    • 0002540844 scopus 로고
    • Note on the class L log L
    • E. M. Stein. (1969). Note on the class L log L. Studia Math. 32: 305-310.
    • (1969) Studia Math. , vol.32 , pp. 305-310
    • Stein, E.M.1
  • 36
    • 84874610061 scopus 로고    scopus 로고
    • A Survey on recent results of the mathematical seminar in Perugia, inspired by the work of professor P.L. Butzer
    • C. Vinti. (1998). A Survey on Recent Results of the Mathematical Seminar in Perugia, inspired by the Work of Professor P.L. Butzer. Result. Math. 34: 32-55.
    • (1998) Result. Math. , vol.34 , pp. 32-55
    • Vinti, C.1
  • 37
    • 27844511616 scopus 로고    scopus 로고
    • A general approximation result for nonlinear integral operators and applications to signal processing
    • G. Vinti. (2001). A general approximation result for nonlinear integral operators and applications to signal processing. Appl. Anal. 79: 217-238.
    • (2001) Appl. Anal. , vol.79 , pp. 217-238
    • Vinti, G.1
  • 38
    • 70449519405 scopus 로고    scopus 로고
    • Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz Spaces
    • G. Vinti. and, L. Zampogni. (2009). Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz Spaces. J. Approx. Theory 161: 511-528.
    • (2009) J. Approx. Theory , vol.161 , pp. 511-528
    • Vinti, G.1    Zampogni, L.2


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