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Volumn 126, Issue 9, 1998, Pages 2677-2686

Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The lp-theory

Author keywords

Non uniform sampling; Riesz basis; Shift invarient spaces

Indexed keywords


EID: 22044438232     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9939-98-04319-6     Document Type: Article
Times cited : (108)

References (25)
  • 1
    • 21344460630 scopus 로고    scopus 로고
    • Oblique projections in atomic spaces
    • MR 961:42020
    • A. Aldroubi. Oblique projections in atomic spaces. Froc. Amer. Math. Soc., 124:2051-2060, 1996. MR 961:42020
    • (1996) Froc. Amer. Math. Soc. , vol.124 , pp. 2051-2060
    • Aldroubi, A.1
  • 2
    • 0002054742 scopus 로고
    • Families of wavelet transforms in connection with Shannon's sampling theory and the Gabor transform
    • O.K. Chui, ed., Academic Press, San Diego, CA, MR 93a:94003
    • A. Aldroubi and M. Unser. Families of wavelet transforms in connection with Shannon's sampling theory and the Gabor transform. In Wavelets: A Tutorial in Theory and Applications, O.K. Chui, ed., Pages 509-528, Academic Press, San Diego, CA, 1992. MR 93a:94003
    • (1992) Wavelets: a Tutorial in Theory and Applications , pp. 509-528
    • Aldroubi, A.1    Unser, M.2
  • 3
    • 84963429212 scopus 로고
    • Families of multiresolution and wavelet spaces with optimal properties
    • MR 94j:42045
    • A. Aldroubi and M. Unser. Families of multiresolution and wavelet spaces with optimal properties. Numer. Fund. Anal, and Optimiz., 14(5):417-446, 1993. MR 94j:42045
    • (1993) Numer. Fund. Anal, and Optimiz. , vol.14 , Issue.5 , pp. 417-446
    • Aldroubi, A.1    Unser, M.2
  • 4
    • 84941053642 scopus 로고
    • Sampling procedure in function spaces and asymptotic equivalence with Shannon's sampling theory
    • MR 95a:94002
    • A. Aldroubi and M. Unser. Sampling procedure in function spaces and asymptotic equivalence with Shannon's sampling theory. Numer. Funct. Anal, and Optimiz., 15(1):1-21, 1994. MR 95a:94002
    • (1994) Numer. Funct. Anal, and Optimiz. , vol.15 , Issue.1 , pp. 1-21
    • Aldroubi, A.1    Unser, M.2
  • 5
    • 0026910575 scopus 로고
    • Cardinal spline filters: Stability and convergence to the ideal sine interpolator
    • A. Aldroubi, M. Unser, and M. Eden. Cardinal spline filters: Stability and convergence to the ideal sine interpolator. Signal Processing, 28:127-138, 1992.
    • (1992) Signal Processing , vol.28 , pp. 127-138
    • Aldroubi, A.1    Unser, M.2    Eden, M.3
  • 6
    • 0002237285 scopus 로고
    • Irregular sampling and frames Wavelets
    • O.K. Chui, ed., MR 93c:42030
    • J.J. Benedetto. Irregular sampling and frames. In Wavelets: A Tutorial in Theory and Applications, O.K. Chui, ed., Pages 445-507, Academic Press, San Diego, CA, 1992. MR 93c:42030
    • (1992) Tutorial in Theory and Applications , pp. 445-507
    • Benedetto, J.J.1
  • 7
    • 84966227164 scopus 로고
    • Some notes on an expansion theorem of Paley and Wiener
    • MR 4:97e
    • R.J. Duffin and J.J. Eachus. Some notes on an expansion theorem of Paley and Wiener. Bull. Amer. Math. Soc., 48:850-855, 1942. MR 4:97e
    • (1942) Bull. Amer. Math. Soc. , vol.48 , pp. 850-855
    • Duffin, R.J.1    Eachus, J.J.2
  • 8
    • 0001433314 scopus 로고
    • Banach convolution algebras of Wiener type
    • Amsterdam-Oxford-New York, Colloquia Math. Soc. J. Bolyai, North Holland Publ. Co. MR 85j:43005
    • H.G. Feichtinger. Banach convolution algebras of Wiener type. In Proc. ConJ. Functions, Series, Operators, Budapest, pages 509-524, Amsterdam-Oxford-New York, 1980. Colloquia Math. Soc. J. Bolyai, North Holland Publ. Co. MR 85j:43005
    • (1980) Proc. ConJ. Functions, Series, Operators, Budapest
    • Feichtinger, H.G.1
  • 9
    • 0001656814 scopus 로고
    • Generalized amalgams, with applications to Fourier transform
    • MR 92f:46038
    • H.G. Feichtinger. Generalized amalgams, with applications to Fourier transform. Can. J. of Math., 42(3):395-409, 1990. MR 92f:46038
    • (1990) Can. J. of Math. , vol.42 , Issue.3 , pp. 395-409
    • Feichtinger, H.G.1
  • 10
    • 0001267371 scopus 로고    scopus 로고
    • New results on regular and
    • K. Jarosz, editor, Edwardsville, IL, April 1990, 1991. Marcel Dekker. MR 93c:46038a
    • H.G. Feichtinger. New results on regular and irregular sampling based on Wiener amalgams. In K. Jarosz, editor,Proc. Conf. Function Spaces, volume 136 of Lect. Notes in Pure and Appi Math, pages 107-122, Edwardsville, IL, April 1990, 1991. Marcel Dekker. MR 93c:46038a
    • Proc. Conf. Function Spaces, Volume 136 of Lect. Notes in Pure and Appi Math , vol.136
    • Feichtinger, H.G.1
  • 11
    • 0037490442 scopus 로고
    • Wiener amalgams over Euclidean spaces and some of their applications
    • K. Jarosz, editor, Edwardsville, IL, April 1990, Marcel Dekker. MR93c:46038b
    • H.G. Feichtinger. Wiener amalgams over Euclidean spaces and some of their applications. In K. Jarosz, editor,Proc. Conf. Function Spaces, volume 136 of Lect. Notes in Pure and Appl. Math., pages 123-137, Edwardsville, IL, April 1990, 1991. Marcel Dekker. MR93c:46038b
    • (1991) Proc. Conf. Function Spaces, Volume 136 of Lect. Notes in Pure and Appl. Math. , vol.136 , pp. 123-137
    • Feichtinger, H.G.1
  • 12
    • 0000741361 scopus 로고
    • Non-orthogonal wavelet and Gabor expansions
    • M.B. Ruskai, G. Beylkin, R.R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and L. Raphael, eds., Jones and Bartlett, Boston, MR 93k:42017
    • H.G. Feichtinger and K. Gröchenig. Non-orthogonal wavelet and Gabor expansions, and group representations. In Wavelets and their Applications,M.B. Ruskai, G. Beylkin, R.R. Coifman, I. Daubechies, S. Mallat, Y. Meyer, and L. Raphael, eds., Pages 353-375, Jones and Bartlett, Boston, 1992. MR 93k:42017
    • (1992) Wavelets and Their Applications
    • Feichtinger, H.G.1    Gröchenig, K.2    Representations, G.3
  • 13
    • 0000979681 scopus 로고
    • Iterative reconstruction of multivariate band-limited functions from irregular sampling values
    • MR 93a:94006
    • H.G. Feichtinger and K. Gröchenig. Iterative reconstruction of multivariate band-limited functions from irregular sampling values. SIAM J. Math. Anal. 231:244-261, 1992. MR 93a:94006
    • (1992) SIAM J. Math. Anal. , vol.231 , pp. 244-261
    • Feichtinger, H.G.1    Gröchenig, K.2
  • 14
    • 84968515233 scopus 로고
    • Five short stories about the cardinal series
    • MR 86k:42045
    • J.R. Higgins. Five short stories about the cardinal series. Bull. Amer. Math. Soc., 121:45-89, 1985. MR 86k:42045
    • (1985) Bull. Amer. Math. Soc. , vol.121 , pp. 45-89
    • Higgins, J.R.1
  • 15
    • 0017558676 scopus 로고
    • The Shannon sampling theorem-its various extensions and applications: A tutorial review
    • A.J. Jerri. The Shannon sampling theorem-its various extensions and applications: A tutorial review. Proc. IEEE, 65:1565-1596,1977.
    • (1977) Proc. IEEE , vol.65 , pp. 1565-1596
    • Jerri, A.J.1
  • 16
    • 0000701478 scopus 로고
    • The exact value of the Paley-Wiener constant
    • MR 28:5289
    • M.I. Kadec. The exact value of the Paley-Wiener constant. Soviet Math. Doklady, 5:559-561, 1964. MR 28:5289
    • (1964) Soviet Math. Doklady , vol.5 , pp. 559-561
    • Kadec, M.I.1
  • 18
    • 0030104822 scopus 로고    scopus 로고
    • Irregular sampling for spline ' wavelet subspaces
    • MR 97b:94006
    • Y. Liu. Irregular sampling for spline ' wavelet subspaces. IEEE Trans. Inform. Theory, 42(2):623-627, 1996. MR 97b:94006
    • (1996) IEEE Trans. Inform. Theory , vol.42 , Issue.2 , pp. 623-627
    • Liu, Y.1
  • 20
    • 84911837213 scopus 로고
    • Communications in the presence of noise
    • MR 10:464e
    • C.E. Shannon. Communications in the presence of noise. Proc. IRE, 37:10-21, 1949. MR 10:464e
    • (1949) Proc. IRE , vol.37 , pp. 10-21
    • Shannon, C.E.1
  • 21
    • 0028546247 scopus 로고
    • A general sampling theory for non-ideal acquisition devices
    • M. Unser and A. Aldroubi. A general sampling theory for non-ideal acquisition devices. IEEE Trans, On Signal Processing, 42(11):2915-2925,1994.
    • (1994) IEEE Trans, on Signal Processing , vol.42 , Issue.11 , pp. 2915-2925
    • Unser, M.1    Aldroubi, A.2
  • 22
    • 0026743698 scopus 로고
    • Polynomial spline signal approximations: Filter design and asymptotic equivalence with Shannon's sampling theorem
    • CMP 92:07
    • M. Unser, A. Aldroubi, and M. Eden. Polynomial spline signal approximations: filter design and asymptotic equivalence with Shannon's sampling theorem. IEEE Trans. Image Process., 38:95-103, 1991. CMP 92:07
    • (1991) IEEE Trans. Image Process. , vol.38 , pp. 95-103
    • Unser, M.1    Aldroubi, A.2    Eden, M.3
  • 24
    • 0000687222 scopus 로고
    • Application of Reproducing Kernel Hubert Spaces-bandlimited signal models
    • K. Yao. Application of Reproducing Kernel Hubert Spaces-bandlimited signal models. Information and Control, 11:429-444, 1967.
    • (1967) Information and Control , vol.11 , pp. 429-444
    • Yao, K.1
  • 25
    • 0026141901 scopus 로고
    • On Kramer's sampling theorem associated with general Sturm-Liouville problems and Lagrange interpolation
    • MR 92b:34038
    • A.I. Zayed. On Kramer's sampling theorem associated with general Sturm-Liouville problems and Lagrange interpolation. SIAM J. Appl. Math., 51:575-604, 1991. MR 92b:34038
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 575-604
    • Zayed, A.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.