Wavelet Thresholding Techniques for Power Spectrum Estimation

IEEE Transactions on Signal Processing

Volumn 42, Issue 11, 1994, Pages 3126-3136

  Moulin, Pierre ^a  

^a TELCORDIA TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FREQUENCY RESPONSE; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION; RANDOM PROCESSES; SIGNAL FILTERING AND PREDICTION; SPEECH ANALYSIS; SPEECH PROCESSING; STATISTICAL METHODS;

ADDITIVE NON GAUSSIAN NOISE; DIFFERENT RESOLUTION LEVELS; GAUSSIAN DISTRIBUTION; INDEPENDENT RANDOM VARIABLES; LOG PERIODOGRAM; LOGARITHM; NARROW SPECTRAL BANDWIDTH; NOISE COEFFICIENT; SIGNAL CORRUPTION; WAVELET THRESHOLDING TECHNIQUES;

SPECTRUM ANALYSIS;

EID: 0028546119     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.330372     Document Type: Article

References (37)

1. Y. Chow and U. Grenander, “A sieve method for the spectral density,” Annals Statist., vol. 13, no. 3, pp. 998–1010, 1985.
2. P. Moulin, J. A. O’Sullivan, and D. L. Snyder, “A method of sieves for multiresolution spectrum estimation and radar imaging,” IEEE Trans. Inform. Theory, Special Issue on Wavelet Transforms and Multiresolution Analysis, vol. 38, pp. 801–813, 1992.
3. R. Cogburn and H. T. Davis, “Periodic splines and spectral estimation,” Annals Statist., vol. 2, no. 6, pp. 1108–1126, 1974.
4. G. Wahba and S. Wold, “Periodic splines for spectral density estimation: The use of cross validation for determining the degree of smoothing,” Commun. Statist., vol. 4, no. 2, pp. 125–141, 1975.
5. G. Wahba, “Automatic smoothing of the log periodogram,” J. Am. Statist. Assoc., vol. 75, no. 369, pp. 122–132, 1980.
6. D. R. Brillinger, Time Series Data Analysis and Theory. New York: Holt, 1975.
7. M. B. Priestley, Spectral Analysis of Time Series, vol. I. London, U.K.: Academic, 1981.
8. G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications. Oakland, CA: Holden-Day, 1968.
9. J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE, vol. 57, pp. 1408–1418, 1969.
10. L. R. Rabiner and R. W. Schafer, Digital Processing of Speech Signals. Englewood Cliffs, NJ: Prentice-Hall, 1978.
11. S. G. Mallat and W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inform. Theory, Special Issue on Wavelet Transforms and Multiresolution Analysis, vol. 38, pp. 617–643, 1992.
12. J. Lu et al., “Noise reduction with a multiscale edge representation and perceptual criteria,” in Proc. IEEE Int. Symp. Time-Frequency, Time-Scale Anal. (Victoria, B.C., Canada), 1992, pp. 555–558.
13. D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Dept. of Statistics, Stanford Univ., Stanford, CA, Tech. Rep., 1992.
14. D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: Asymptotia?,” Dept. of Statistics, Stanford Univ., Stanford, CA, Tech. Rep., 1992.
15. D. L. Donoho, “De-noising by soft-thresholding,” Dept. of Statistics, Stanford Univ., Stanford, CA, Tech. Rep., 1992.
16. D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Dept. of Statistics. Stanford Univ., CA, Tech. Rep., 1992.
17. I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Estimation d’une densité de probabilité par meéthode d’ondelettes,” Comptes Rendus de 1'Acadeémie des Sciences de Paris (A), vol. 315, pp. 211–216, 1992.
18. P. Moulin, “A wavelet regularization method for diffuse radar-target imaging and speckle-noise reduction,” J. Math. Imaging, Vision, Special Issue on Wavelets, vol. 3, no. 1, pp. 123–134, 1993.
19. D. J. Thompson, “Spectrum estimation and harmonic analysis,” Proc. IEEE. vol. 70, pp. 1055–1096, 1982.
20. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I. New York: Wiley, 1968.
21. H.-Y. Gao, “Choice of thresholds for wavelet estimation of the log spectrum,” preprint, Dept. of Statistics, Univ. Califomia-Berkeley, 1993.
22. N. Reid, “Saddlepoint methods and statistical inference,” Statist. Sci., vol. 3. no. 2, pp. 213–238, 1988.
23. R. Lugannani and S. Rice, “Saddle point approximation for the distribution of the sum of independent random variables,” Adv. Appl. Probability, vol. 12, pp. 475–490, 1980.
24. H. E. Daniels, “Tail probability approximations,” Int. Statist. Rev., vol. 55, no. 1, pp. 37–48, 1987.
25. H. D. Brunk, “Bayes least squares linear regression is asymptotically full Bayes: Estimation of spectral densities,” in Topics in Non-Gaussian Signal Processing, E. J. Wegman, S. C. Schwartz, and J. B. Thomas, Eds. Berlin, Germany: Springer-Verlag, 1991, pp. 128–147.
26. D. R. Brillinger, “The key role of tapering in spectrum estimation,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 1075–1076, 1981.
27. W. H. Press et al., Numerical Recipes in C. Cambridge, U.K.: Cambridge University Press, 1990.
28. W. C. Jakes, Jr., “Mobile radio propagation,” in Microwave Mobile Communications, W. C. Jakes, Jr., Ed. New York: Wiley, 1974, ch. 1.
29. I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Series in Appl. Math. Philadelphia, PA: SIAM, 1992.
30. I. Daubechies, “Orthonormal bases of compactly supported wavelets II. Variations on a theme,” SIAM J. Math, Anal., vol. 24, no. 2, pp. 499–519, Mar. 1993.
31. W. Feller, An Introduction to Probability Theory and Its Applications, vol. II. New York: Wiley, 1966.
32. S. G. Mallat, “Multiresolution approximations and wavelet orthonormal bases of L2(R),” Trans. Amer. Math. Soc., vol. 315, no. 1, pp. 69–87, 1989.
33. W. Hardle, Applied Nonparametric Regression. Cambridge U.K.: Cambridge University Press, 1990.
34. A. Cohen, I. Daubechies, and P. Vial, “Wavelets on the interval and fast wavelet transforms,” J. Appl., Computational Harmonic Anal., 1993.
35. S. R. S. Varadhan, Large Deviations and Applications, CBMS-NSF Regional Conference Series in Applied Math. Philadelphia, PA: SIAM, 1984.
36. M. Basseville et al., “Modeling and estimation of multiresolution stochastic processes,” IEEE Trans. Inform. Theory, Special Issue on Wavelet Transforms and Multiresolution Analysis, vol. 38, pp. 766–784, 1992.
37. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York: Dover, 1972.