On denoising and best signal representation

IEEE Transactions on Information Theory

Volumn 45, Issue 7, 1999, Pages 2225-2238

  Krim, Hamid ^a,b   Tucker, Dewey ^a,c   Mallat, Stéphane ^a,d   Donoho, David ^a,e  

^a IEEE

^b North Carolina State University   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^e STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; HEURISTIC METHODS; SPURIOUS SIGNAL NOISE; WHITE NOISE;

BEST BASIS ALGORITHMS; SIGNAL REPRESENTATION; WHITE GAUSSIAN NOISE;

SIGNAL RECONSTRUCTION;

EID: 0033344876     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.796365     Document Type: Article

References (17)

1. P. J. Bickel and K. A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics. Oakland, CA: Holden-Day, 1977.
2. R. Coifman and Y. Meyer, "Remarques sur l'analyse de Fourierá fenêtre," C. R. Acad. Sci. Sér. I, pp. 259-261, 1991.
3. R. R. Coifman and M. V. Wickerhauser, "Entropy-based algorithms for best basis selection," IEEE Trans. Inform. Theory, vol. 38, pp. 713-718, Mar. 1992.
4. I. Daubechies, "Orthonormal bases of compactly supported wavelets," Com. Pure and Appl. Math., vol. XLI, pp. 909-996, 1988.
5. D. Donoho and I. Johnstone, "Ideal denoising in an orthogonal basis chosen from a library of bases," C. R. Acad. Sci. Paris, Oct. 1994.
6. _, "Ideal spatial adaptation by wavelet shrinkage," Dept. Stat., Stanford Univ., June 1992, preprint.
7. B. Gnedenko, "Sur la distribution limite du terme maximum d'une serie aleatoire," Ann. Math., vol. 44, no. 3, pp. 423-453, July 1943.
8. H. Krim, S. Mallat, D. Donoho, and A. Willsky, "Best basis algorithm for signal enhancement," in IEEE, Int. Conf. Acoustics, Speech and Signal Processing ASSP'95 (Detroit, MI, May 1995).
9. H. Krim and J.-C. Pesquet, "On the statistics of best bases criteria," in Wavelets in Statistics of Lecture Notes in Statistics. New York: Springer-Verlag, July 1995, pp. 193-207.
10. S. Mallat, "A theory for multiresolution signal decomposition: The wavelet representation," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, July 1989.
11. _, A Wavelet Tour of Signal Processing. Boston, MA: Academic, 1998.
12. H. Malvar, "Lapped transforms for efficient transform subband coding," IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 969-978, June 1990.
13. A. W. Marshall and I. Olkin, Inequalities: Theory and Majorization and Its Applications. New York: Academic, 1979.
14. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.
15. S. I. Resnick, "Extreme values, regular variation and point processes," Appl. Probab., 1987.
16. C. M. Stein, "Estimation of the mean of a multivariate normal distribution," Ann. Statist., vol. 9, no. 6, pp. 1135-1151, 1981.
17. M. V. Wickerhauser, "INRIA lectures on wavelet packet algorithms," Ondelettes et Paquets D'ondelettes, Roquencourt, France, June 17-21, 1991, pp. 31-99.