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Volumn 55, Issue 1, 2009, Pages 374-400

Representation and compression of multidimensional piecewise functions using surflets

Author keywords

Compression; Discontinuities; Metric entropy; Multidimensional signals; Multiscale representations; Nonlinear approximation; Rate distortion; Sparse representations; Surflets; Wavelets

Indexed keywords

ASYMPTOTIC ANALYSIS; CELLULAR RADIO SYSTEMS; EDGE DETECTION; ELECTRIC DISTORTION; ENTROPY; FUNCTIONAL ANALYSIS; IMAGE CODING; MOTION ESTIMATION; POLYNOMIAL APPROXIMATION; PROBABILITY DENSITY FUNCTION; SIGNAL DISTORTION; VIDEO RECORDING;

EID: 58249141985     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.2008153     Document Type: Article
Times cited : (34)

References (33)
  • 2
    • 5044248869 scopus 로고    scopus 로고
    • Surflets: A sparse representation for multidimensional functions containing smooth discontinuities
    • Chicago, IL, Jun./Jul
    • V. Chandrasekaran, M. B. Wakin, D. Baron, and R. Baraniuk, "Surflets: A sparse representation for multidimensional functions containing smooth discontinuities," in Proc. IEEE Int. Symp. Information Theory (ISIT2004), Chicago, IL, Jun./Jul. 2004, p. 563.
    • (2004) Proc. IEEE Int. Symp. Information Theory (ISIT2004) , pp. 563
    • Chandrasekaran, V.1    Wakin, M.B.2    Baron, D.3    Baraniuk, R.4
  • 3
    • 0026727407 scopus 로고
    • Image compression through wavelet transform coding
    • Mar
    • R. A. DeVore, B. Jawerth, and B. J. Lucier, "Image compression through wavelet transform coding," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 719-746, Mar. 1992.
    • (1992) IEEE Trans. Inf. Theory , vol.38 , Issue.2 , pp. 719-746
    • DeVore, R.A.1    Jawerth, B.2    Lucier, B.J.3
  • 4
    • 0027798110 scopus 로고
    • Embedded image coding using zerotrees of wavelet coefficients
    • Dec
    • J. Shapiro, "Embedded image coding using zerotrees of wavelet coefficients," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3445-3462, Dec. 1993.
    • (1993) IEEE Trans. Signal Process , vol.41 , Issue.12 , pp. 3445-3462
    • Shapiro, J.1
  • 5
    • 0031146030 scopus 로고    scopus 로고
    • Space-frequency quantization for wavelet image coding
    • May
    • Z. Xiong, K. Ramchandran, and M. T. Orchard, "Space-frequency quantization for wavelet image coding," IEEE Trans. Image Process. vol. 6, no. 5, pp. 677-693, May 1997.
    • (1997) IEEE Trans. Image Process , vol.6 , Issue.5 , pp. 677-693
    • Xiong, Z.1    Ramchandran, K.2    Orchard, M.T.3
  • 6
    • 0036649527 scopus 로고    scopus 로고
    • On the importance of combining wavelet-based nonlinear approximation with coding strategies
    • Jul
    • A. Cohen, I. Daubechies, O. G. Guleryuz, and M. T. Orchard, "On the importance of combining wavelet-based nonlinear approximation with coding strategies," IEEE Trans. Inf. Theory, vol. 48, no. 7, pp. 1895-1921, Jul. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.7 , pp. 1895-1921
    • Cohen, A.1    Daubechies, I.2    Guleryuz, O.G.3    Orchard, M.T.4
  • 7
    • 0029307534 scopus 로고
    • Denoising by soft-thresholding
    • May
    • D. L. Donoho, "Denoising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
    • (1995) IEEE Trans. Inf. Theory , vol.41 , Issue.3 , pp. 613-627
    • Donoho, D.L.1
  • 8
    • 0033248623 scopus 로고    scopus 로고
    • Wedgelets: Nearly-minimax estimation of edges
    • D. L. Donoho, "Wedgelets: Nearly-minimax estimation of edges," Ann. Statist., vol. 27, pp. 859-897, 1999.
    • (1999) Ann. Statist , vol.27 , pp. 859-897
    • Donoho, D.L.1
  • 9
    • 0033344876 scopus 로고    scopus 로고
    • On denoising and best signal representation
    • Nov
    • H. Krim, D. Tucker, S. Mallat, and D. Donoho, "On denoising and best signal representation," IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 2225-2238, Nov. 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.45 , Issue.7 , pp. 2225-2238
    • Krim, H.1    Tucker, D.2    Mallat, S.3    Donoho, D.4
  • 10
    • 0038321621 scopus 로고    scopus 로고
    • Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging
    • Mar
    • R. Willett and R. Nowak, "Platelets: A multiscale approach for recovering edges and surfaces in photon-limited medical imaging," IEEE Trans. Med. Imag., vol. 22, no. 3, pp. 332-350, Mar. 2003.
    • (2003) IEEE Trans. Med. Imag , vol.22 , Issue.3 , pp. 332-350
    • Willett, R.1    Nowak, R.2
  • 11
    • 0033234630 scopus 로고    scopus 로고
    • Smooth discrimination analysis
    • E. Mammen and A. B. Tsybakov, "Smooth discrimination analysis," Ann. Statist., vol. 27, pp. 1808-1829, 1999.
    • (1999) Ann. Statist , vol.27 , pp. 1808-1829
    • Mammen, E.1    Tsybakov, A.B.2
  • 12
    • 3142725508 scopus 로고    scopus 로고
    • Optimal aggregation of classifiers in statistical learning
    • A. B. Tsybakov, "Optimal aggregation of classifiers in statistical learning," Ann. Statist., vol. 32, no. 1, pp. 135-166, 2004.
    • (2004) Ann. Statist , vol.32 , Issue.1 , pp. 135-166
    • Tsybakov, A.B.1
  • 13
    • 0025482241 scopus 로고
    • The wavelet transform, time-frequency localization and signal analysis
    • Sep
    • I. Daubechies, "The wavelet transform, time-frequency localization and signal analysis," IEEE Trans. Inf. Theory, vol. 36, no. 5, pp. 961-1005, Sep. 1990.
    • (1990) IEEE Trans. Inf. Theory , vol.36 , Issue.5 , pp. 961-1005
    • Daubechies, I.1
  • 15
    • 0026624134 scopus 로고    scopus 로고
    • n, IEEE Trans. Inf. Theory, 38, no. 2, pt. 2, pp. 533-555, Mar. 1992.
    • n," IEEE Trans. Inf. Theory, vol. 38, no. 2, pt. 2, pp. 533-555, Mar. 1992.
  • 16
    • 0003306887 scopus 로고    scopus 로고
    • Curvelets - A suprisingly effective nonadaptive representation for objects with edges
    • E. J. Candès and D. L. Donoho, A. Cohen, C. Rabut, and L. L. Schumaker, Eds, Nashville, TN: Vanderbilt Univ. Press
    • E. J. Candès and D. L. Donoho, A. Cohen, C. Rabut, and L. L. Schumaker, Eds., "Curvelets - A suprisingly effective nonadaptive representation for objects with edges," in Curve and Surface Fitting Nashville, TN: Vanderbilt Univ. Press, 1999.
    • (1999) Curve and Surface Fitting
  • 20
    • 58249136378 scopus 로고    scopus 로고
    • A. N. Kolmogorov and V. M. Tihomirov, ∈-entropy and ∈-capacity of sets in functional spaces, Amer. Math. Soc. Transl. (Ser. 2), 17, pp. 277-364, 1961.
    • A. N. Kolmogorov and V. M. Tihomirov, "∈-entropy and ∈-capacity of sets in functional spaces," Amer. Math. Soc. Transl. (Ser. 2), vol. 17, pp. 277-364, 1961.
  • 21
    • 0009030508 scopus 로고
    • Entropies of several sets of real valued functions
    • G. F. Clements, "Entropies of several sets of real valued functions," Pacific J. Math., vol. 13, pp. 1085-1095, 1963.
    • (1963) Pacific J. Math , vol.13 , pp. 1085-1095
    • Clements, G.F.1
  • 23
    • 33645986468 scopus 로고    scopus 로고
    • Wavelet-domain approximation and compression of piecewise smooth images
    • May
    • M. B. Wakin, J. K. Romberg, H. Choi, and R. G. Baraniuk, "Wavelet-domain approximation and compression of piecewise smooth images," IEEE Trans. Image Process., vol. 15, no. 5, pp. 1071-1087, May 2006.
    • (2006) IEEE Trans. Image Process , vol.15 , Issue.5 , pp. 1071-1087
    • Wakin, M.B.1    Romberg, J.K.2    Choi, H.3    Baraniuk, R.G.4
  • 24
    • 46149112635 scopus 로고    scopus 로고
    • Effective coding of images with the use of geometrical wavelets
    • in Polish, Zakopane, Poland
    • A. Lisowska, "Effective coding of images with the use of geometrical wavelets," in Proc. Decision Support Systems Conf. (in Polish), Zakopane, Poland, 2003.
    • (2003) Proc. Decision Support Systems Conf
    • Lisowska, A.1
  • 25
    • 34047217222 scopus 로고    scopus 로고
    • Multidimensional directional filter banks and surfacelets
    • Apr
    • Y. Lu and M. N. Do, "Multidimensional directional filter banks and surfacelets," IEEE Trans. Image Process., vol. 16, no. 4, pp. 918-931, Apr. 2007.
    • (2007) IEEE Trans. Image Process , vol.16 , Issue.4 , pp. 918-931
    • Lu, Y.1    Do, M.N.2
  • 28
    • 58249130153 scopus 로고    scopus 로고
    • Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis Rice Univ. ECE Dep., Houston, TX
    • Tech. Rep, Mar
    • V. Chandrasekaran, M. Wakin, D. Baron, and R. Baraniuk, Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis Rice Univ. ECE Dep., Houston, TX, Tech. Rep., Mar. 2004.
    • (2004)
    • Chandrasekaran, V.1    Wakin, M.2    Baron, D.3    Baraniuk, R.4
  • 32
    • 0029307102 scopus 로고
    • The context-tree weighting method: Basic properties
    • May
    • F. M. J.Willems, Y. M. Shtarkov, and T. J. Tjalkens, "The context-tree weighting method: Basic properties," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 653-664, May 1995.
    • (1995) IEEE Trans. Inf. Theory , vol.41 , Issue.3 , pp. 653-664
    • Willems, F.M.J.1    Shtarkov, Y.M.2    Tjalkens, T.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.