메뉴 건너뛰기




Volumn 59, Issue 3, 1997, Pages 603-613

Fractal function estimation via wavelet shrinkage

Author keywords

Fractal Dimension; Fractal Function; Rough Function; Wavelets

Indexed keywords


EID: 0009279326     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00085     Document Type: Article
Times cited : (16)

References (32)
  • 4
    • 0000213760 scopus 로고
    • Multiresolution analysis, wavelets, and fast algorithms on an interval
    • Cohen, A., Daubechies, I., Jawerth, B. and Vial, P. (1993) Multiresolution analysis, wavelets, and fast algorithms on an interval. C. R. Acad. Sci. Paris A, 316, 417-421.
    • (1993) C. R. Acad. Sci. Paris A , vol.316 , pp. 417-421
    • Cohen, A.1    Daubechies, I.2    Jawerth, B.3    Vial, P.4
  • 5
    • 0001884067 scopus 로고
    • Characterizing surface smoothness via estimation of effective fractal dimension
    • Constantine, A. G. and Hall, P. (1994) Characterizing surface smoothness via estimation of effective fractal dimension. J. R. Statist. Soc. B, 56, 97-113.
    • (1994) J. R. Statist. Soc. B , vol.56 , pp. 97-113
    • Constantine, A.G.1    Hall, P.2
  • 6
    • 0003833285 scopus 로고
    • Philadelphia: Society for Industrial and Applied Mathematics
    • Daubechies, I. (1992) Ten Lecture on Wavelets. Philadelphia: Society for Industrial and Applied Mathematics.
    • (1992) Ten Lecture on Wavelets
    • Daubechies, I.1
  • 7
    • 85013565266 scopus 로고
    • Two recent results on wavelets: Wavelet bases for the interval, and biorthogonal wavelet diagonalizing the derivative operator
    • (eds L. L. Schumaker and G. Webb), New York: Academic Press
    • _(1994) Two recent results on wavelets: wavelet bases for the interval, and biorthogonal wavelet diagonalizing the derivative operator. In Recent Advances in Wavelet Analysis (eds L. L. Schumaker and G. Webb), pp. 237-257. New York: Academic Press.
    • (1994) Recent Advances in Wavelet Analysis , pp. 237-257
  • 8
    • 0027873602 scopus 로고
    • Unconditional bases are optimal bases for data compression and for statistical estimation
    • Donoho, D. L. (1993a) Unconditional bases are optimal bases for data compression and for statistical estimation. Appl. Comput. Harmon. Anal., 1, 100-115.
    • (1993) Appl. Comput. Harmon. Anal. , vol.1 , pp. 100-115
    • Donoho, D.L.1
  • 9
    • 0002190659 scopus 로고
    • Smooth wavelet decompositions with blocky coefficient kernels
    • (eds L. L. Schumaker and G. Webb), New York: Academic Press
    • _(1993b) Smooth wavelet decompositions with blocky coefficient kernels. In Recent Advances in Wavelet Analysis (eds L. L. Schumaker and G. Webb), pp. 259-308. New York: Academic Press.
    • (1993) Recent Advances in Wavelet Analysis , pp. 259-308
  • 10
    • 18244393924 scopus 로고
    • Interpolating wavelet transformations
    • Department of Statistics, Stanford University, Stanford
    • _(1994) Interpolating wavelet transformations. Technical Report. Department of Statistics, Stanford University, Stanford.
    • (1994) Technical Report
  • 11
    • 0029307534 scopus 로고
    • De-noising by soft thresholding
    • _(1995) De-noising by soft thresholding. IEEE Trans. Inform. Theory, 41, 613-627.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 613-627
  • 12
    • 0041958932 scopus 로고
    • Ideal spatial adaptation by wavelet shrinkage
    • Donoho, D. L. and Johnstone, I. M. (1994) Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81, 425-455.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 13
    • 84950459514 scopus 로고
    • Adapting to unknown smoothness via wavelet shrinkage
    • _(1995) Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Ass., 90, 1200-1224.
    • (1995) J. Am. Statist. Ass. , vol.90 , pp. 1200-1224
  • 14
    • 18244378952 scopus 로고    scopus 로고
    • Minimax estimation via wavelet shrinkage
    • to be published
    • _(1996) Minimax estimation via wavelet shrinkage. Ann. Statist., to be published.
    • (1996) Ann. Statist.
  • 18
    • 0029326090 scopus 로고
    • On the effect of measuring a self-similar process
    • Hall, P. (1995) On the effect of measuring a self-similar process. SIAM J. Appl. Math., 55, 800-808.
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 800-808
    • Hall, P.1
  • 19
    • 0000413704 scopus 로고
    • On the performance of box-counting estimators of fractal dimension
    • Hall, P. and Wood, A. (1993) On the performance of box-counting estimators of fractal dimension. Biometrika, 80, 246-252.
    • (1993) Biometrika , vol.80 , pp. 246-252
    • Hall, P.1    Wood, A.2
  • 20
    • 18244390638 scopus 로고
    • Wavelets and nonlinear analysis
    • (eds J. J. Benedetto and M. W. Frazier), Ann Arbor: CRC
    • Jaffard, S. (1994) Wavelets and nonlinear analysis. In Wavelets: Mathematics and Applications (eds J. J. Benedetto and M. W. Frazier), pp. 467-503. Ann Arbor: CRC.
    • (1994) Wavelets: Mathematics and Applications , pp. 467-503
    • Jaffard, S.1
  • 21
    • 0000621736 scopus 로고
    • Noise reduction in dynamical systems
    • Kostelich, E. and Yorke, J. A. (1988) Noise reduction in dynamical systems. Phys. Rev. A, 38, 1469-1473.
    • (1988) Phys. Rev. A , vol.38 , pp. 1469-1473
    • Kostelich, E.1    Yorke, J.A.2
  • 25
    • 0000485975 scopus 로고
    • Maximum likelihood estimates of the fractal dimension for random spatial patterns
    • Ogata, Y. and Katsura, K. (1991) Maximum likelihood estimates of the fractal dimension for random spatial patterns. Biometrika, 78, 463-474.
    • (1991) Biometrika , vol.78 , pp. 463-474
    • Ogata, Y.1    Katsura, K.2
  • 27
    • 0001077703 scopus 로고
    • Estimating the dimension of a fractal
    • Taylor, C. C. and Taylor, S. J. (1991) Estimating the dimension of a fractal. J. R. Statist. Soc. B, 53, 353-364.
    • (1991) J. R. Statist. Soc. B , vol.53 , pp. 353-364
    • Taylor, C.C.1    Taylor, S.J.2
  • 29
    • 0000999642 scopus 로고
    • Jump and sharp cusp detection by wavelets
    • Wang, Y. (1995) Jump and sharp cusp detection by wavelets. Biometrika, 82, 385-397.
    • (1995) Biometrika , vol.82 , pp. 385-397
    • Wang, Y.1
  • 30
    • 0030492140 scopus 로고    scopus 로고
    • Function estimation via wavelet shrinkage for long-memory data
    • _(1996) Function estimation via wavelet shrinkage for long-memory data. Ann. Statist., 24, 466-484.
    • (1996) Ann. Statist. , vol.24 , pp. 466-484
  • 31
    • 0025462413 scopus 로고
    • A Karhunen-Loéve-like expansion for l/f processes via wavelets
    • Wornell, G. W. and Oppenheim, A. V. (1990) A Karhunen-Loéve-like expansion for l/f processes via wavelets. IEEE Trans. Inform. Theory, 36, 859-861.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 859-861
    • Wornell, G.W.1    Oppenheim, A.V.2
  • 32
    • 0026829738 scopus 로고
    • Estimation of fractal signals from noisy measurements using wavelets
    • _(1992) Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans. Signal Process., 40, 611-623.
    • (1992) IEEE Trans. Signal Process , vol.40 , pp. 611-623


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.