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Volumn 53, Issue 8, 2005, Pages 2690-2699

Entropy-Based Uncertainty Measures for L2(Rn), l2(Z), and l2(Z/NZ) With a Hirschman Optimal Transform for l2(Z/NZ)

Author keywords

Denoising; entropy; time frequency resolution; uncertainty

Indexed keywords


EID: 85008048449     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/TSP.2005.850329     Document Type: Article
Times cited : (35)

References (25)
  • 2
    • 84941428932 scopus 로고    scopus 로고
    • Information theoretic inequalities
    • Nov.
    • A. Dembo, T. M. Cover, and J. A. Thomas, “Information theoretic inequalities,” IEEE Trans. Inf. Theory, vol. 37, no. 6, pp. 1501–1518, Nov. 1999.
    • (1999) IEEE Trans. Inf. Theory , vol.37 , Issue.6 , pp. 1501-1518
    • Dembo, A.1    Cover, T.M.2    Thomas, J.A.3
  • 3
    • 0033746977 scopus 로고    scopus 로고
    • Analysis in a finite time-frequency plane
    • Jun.
    • V. DeBrunner, M. Ozaydm, and T. Przebinda, “Analysis in a finite time-frequency plane,” IEEE Trans. Signal Process., vol. 48, no. 6, pp. 1831–1832, Jun. 2000.
    • (2000) IEEE Trans. Signal Process. , vol.48 , Issue.6 , pp. 1831-1832
    • DeBrunner, V.1    Ozaydm, M.2    Przebinda, T.3
  • 4
    • 0032627106 scopus 로고    scopus 로고
    • Using a new uncertainty measure to determine optimal bases for signal representations
    • Phoenix AZ Mar. 15-19 paper 1575
    • T. Przebinda, V. E. DeBrunner, and M. Özaydm, “Using a new uncertainty measure to determine optimal bases for signal representations,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 3, Phoenix, AZ, Mar. 15-19, 1999, paper 1575, pp. 1365–1368.
    • (1999) Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. , vol.3 , pp. 1365-1368
    • Przebinda, T.1    DeBrunner, V.E.2    Özaydm, M.3
  • 5
    • 0035396621 scopus 로고    scopus 로고
    • The optimal transform for the discrete Hirschman uncertainty principle
    • Jul.
    • T. Przebinda, V. E. DeBrunner, and M. Özaydm, “The optimal transform for the discrete Hirschman uncertainty principle,” IEEE Trans. Inf. Theory, vol. 47, no. 5, pp. 2086–2090, Jul. 2001
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.5 , pp. 2086-2090
    • Przebinda, T.1    DeBrunner, V.E.2    Özaydm, M.3
  • 6
    • 0033677127 scopus 로고    scopus 로고
    • The optimal solutions to the continuous- and discrete-time versions of the Hirschman uncertainty principle
    • Istanbul, Turkey Jun. 5-9 paper 1312
    • V. E. DeBrunner, M. Ozaydm, T. Przebinda, and J. Havlicek, “The optimal solutions to the continuous- and discrete-time versions of the Hirschman uncertainty principle,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 1, Istanbul, Turkey, Jun. 5-9, 2000, paper 1312, pp. 81–84.
    • (2000) Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. , vol.1 , pp. 81-84
    • DeBrunner, V.E.1    Ozaydm, M.2    Przebinda, T.3    Havlicek, J.4
  • 7
    • 4344595247 scopus 로고    scopus 로고
    • An entropy-based uncertainty principle for a locally compact abelian group
    • to be published.
    • M. Özaydm and T. Przebinda, “An entropy-based uncertainty principle for a locally compact abelian group,” J. Functional Anal., pp. 241–252, 2004, to be published.
    • (2004) J. Functional Anal. , pp. 241-252
    • Özaydm, M.1    Przebinda, T.2
  • 8
    • 0001542262 scopus 로고
    • A note on entropy
    • I. I. Hirschman, “A note on entropy,” Amer. J. Math., vol. 79, pp. 152–156, 1957.
    • (1957) Amer. J. Math. , vol.79 , pp. 152-156
    • Hirschman, I.I.1
  • 9
    • 0141987268 scopus 로고
    • The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis
    • New York: Springer-Verlag
    • L. Hormander, The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis. New York: Springer-Verlag, 1983.
    • (1983)
    • Hormander, L.1
  • 10
    • 84940644968 scopus 로고
    • A mathematical theory of communication
    • C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., pp. 379–656, 1948.
    • (1948) Bell Syst. Tech. J. , pp. 379-656
    • Shannon, C.E.1
  • 11
    • 0000898117 scopus 로고
    • Inequalities in Fourier analysis
    • W. Beckner, “Inequalities in Fourier analysis,” Ann. Math., pp. 159–182, 1975.
    • (1975) Ann. Math. , pp. 159-182
    • Beckner, W.1
  • 12
    • 0001491241 scopus 로고
    • Pitt's inequality and uncertainty principle
    • W. Beckner, “Pitt's inequality and uncertainty principle,” Proc. Amer. Math. Soc., pp. 1897–1905, 1995.
    • (1995) Proc. Amer. Math. Soc. , pp. 1897-1905
    • Beckner, W.1
  • 13
    • 0000293183 scopus 로고
    • Theory of communication
    • D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. Lond., vol. 93, no. III, pp. 429–457, 1946.
    • (1946) J. Inst. Elect. Eng. Lond. , vol.93 , Issue.3 , pp. 429-457
    • Gabor, D.1
  • 14
    • 0022098435 scopus 로고
    • Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters
    • Jul.
    • J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 2, no. 7, pp. 1160–1169, Jul. 1985.
    • (1985) J. Opt. Soc. Amer. A, Opt. Image Sci. , vol.2 , Issue.7 , pp. 1160-1169
    • Daugman, J.G.1
  • 15
    • 0001616908 scopus 로고
    • Uncertainty principles and signal recovery
    • D. L. Donoho and P. B. Stark, “Uncertainty principles and signal recovery,” SIAM J. Appl. Math., vol. 49, pp. 906–931, 1989.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 906-931
    • Donoho, D.L.1    Stark, P.B.2
  • 17
    • 0028546119 scopus 로고
    • Wavelet thresholding techniques for power spectrum estimation
    • Nov.
    • P. Moulin, “Wavelet thresholding techniques for power spectrum estimation,” IEEE Trans. Signal Process., vol. 42, no. 11, pp. 3126–3136, Nov. 1994.
    • (1994) IEEE Trans. Signal Process. , vol.42 , Issue.11 , pp. 3126-3136
    • Moulin, P.1
  • 18
    • 0031631082 scopus 로고    scopus 로고
    • Application of basis pursuit in spectrum estimation
    • Seattle, WA May 12-15
    • S. S. Chen and D. L. Donoho, “Application of basis pursuit in spectrum estimation,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., vol. 3, Seattle, WA, May 12-15, 1998, pp. 1865–1868.
    • (1998) Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. , vol.3 , pp. 1865-1868
    • Chen, S.S.1    Donoho, D.L.2
  • 19
    • 0032290298 scopus 로고    scopus 로고
    • Spectrum estimation by wavelet thresholding of multitaper estimators
    • Dec.
    • A. T. Walden, D. B. Percival, and E. J. McCoy, “Spectrum estimation by wavelet thresholding of multitaper estimators,” IEEE Trans. Signal Process., vol. 46, no. 12, pp. 3153–3165, Dec. 1998.
    • (1998) IEEE Trans. Signal Process. , vol.46 , Issue.12 , pp. 3153-3165
    • Walden, A.T.1    Percival, D.B.2    McCoy, E.J.3
  • 20
    • 0041958932 scopus 로고
    • Ideal spatial adaptation via wavelet shrinkage
    • D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation via wavelet shrinkage,” Biometrika, vol. 81, pp. 425–455, 1994.
    • (1994) Biometrika , vol.81 , pp. 425-455
    • Donoho, D.L.1    Johnstone, I.M.2
  • 21
    • 0003794165 scopus 로고    scopus 로고
    • ser. ser. Lecture Notes in Statistics. New York: Springer-Verlag
    • M. Jansen, Noise Reduction by Wavelet Thresholding, ser. ser. Lecture Notes in Statistics. New York: Springer-Verlag, 2001, vol. 161.
    • (2001) Noise Reduction by Wavelet Thresholding , vol.161
    • Jansen, M.1
  • 22
    • 0242554726 scopus 로고    scopus 로고
    • A fast efficient technique for the estimation of frequency: interpretation and generalization
    • Mar.
    • B. G. Quinn, “A fast efficient technique for the estimation of frequency: interpretation and generalization,” Biometrika, vol. 86, no. 1, pp. 213–220, Mar. 1999.
    • (1999) Biometrika , vol.86 , Issue.1 , pp. 213-220
    • Quinn, B.G.1
  • 23
    • 0028539964 scopus 로고
    • Threshold behavior of the maximum-likelihood estimator of frequency
    • Nov.
    • B. G. Quin and P. J. Kootsookos, “Threshold behavior of the maximum-likelihood estimator of frequency,” IEEE Trans. Signal Process., vol. 42, no. 11, pp. 3291–3294, Nov. 1994.
    • (1994) IEEE Trans. Signal Process. , vol.42 , Issue.11 , pp. 3291-3294
    • Quin, B.G.1    Kootsookos, P.J.2
  • 25
    • 0026142897 scopus 로고
    • The JPEG still picture compression standard
    • G. K. Wallace, “The JPEG still picture compression standard,” Commun. ACM, vol. 34, pp. 30–44, 1991.
    • (1991) Commun. ACM , vol.34 , pp. 30-44
    • Wallace, G.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.