Locally stationary covariance and signal estimation with macrotiles

IEEE Transactions on Signal Processing

Volumn 51, Issue 3, 2003, Pages 614-627

  Donoho, David L ^a   Mallat, Stéphane ^b   Von Sachs, Rainer ^c   Samuelides, Yann ^b  

^a STANFORD UNIVERSITY   (United States)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Best basis; Cosine basis; Covariance estimation; Local stationarity; Noise removal; Spectrum estimation

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING; SPURIOUS SIGNAL NOISE;

STATIONARY PROCESSES;

SIGNAL DETECTION;

EID: 0037333724     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2002.808116     Document Type: Article

References (20)

1. D.L. Donoho and I. M. Johnstone, "Ideal spatial adaptation via wavelet shrinkage," Biometrika, vol. 81, pp. 425-455, 1994.
2. _, "Ideal denoising in mn orthonormal basis chosen from a library of bases," Comput. Rend. Acad. Sci. Paris Ser A, vol. 319, pp. 1317-1322, 1994.
3. S. G. Mallat, G. Papanicolaou, and Z. Zhang, "Adaptive covariance estimation of locally stationary processes," Ann. Statist., vol. 26, pp. 1-47, 1998.
4. D. L. Donoho, S. Mallat, and R. von Sachs, "Estimating covariances of locally stationary processes: Rates of convergence of best basis methods," Stanford Univ., Statistics Dept., 517, 1998.
5. E. Moulines, P. Duhamel, J.-F. Cardoso, and S. Mayrargue, "Subspace methods for the blind identification of multichannel FIR filters," IEEE Trans. Signal Processing, vol. 43, pp. 214-224, Feb. 1995.
6. M. B. Priestley, "Evolutionary spectra and nonstationary processes," J. R. Statist. Soc. B, vol. 27, pp. 204-237, 1965.
7. Y. Samuelides, "Macrotile estimation and market model with jumps," Ph.D. dissertation, Ecole Polytechnique, Pads, France, 2001.
8. Y. Samuelides and S. Mallat, "Penalized macrotile estimation of locally stationary covariances," Ann. Statist., 2002, submitted for publication.
9. A. R. Barron, L. Birgé, and P. Massart, "Risk bounds for model selection via penalization," Probab. Theory Relat. Fields, vol. 113, pp. 301-413, 1999.
10. A. R. Barron and T. M. Cover, "Minimum complexity density estimation," IEEE Trans. Inform. Theory, vol. 37, pp. 1034-1054, July 1991.
11. R. R. Coifman and Y. Meyer, "Remarques sur l'analyze de Fourier à fenêtre," Comput. Rend. Acad. Sci. Paris Ser.A, vol. 312, pp. 259-261, 1991.
12. H. S. Malvar and D. H. Staelin, "The LOT: Transform coding without block effects," IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp. 553-559, Apr. 1989.
13. S. G. Mallat, A Wavelet Tour of Signal Processing, 2nd ed. New York: Academic, 1999.
14. L. Breiman, J. Friedman, R. Olshen, and C. Stone, Classification and Regression Trees. London, U.K.: Chapman & Hall, 1993.
15. 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.
16. R. Dahlhaus, "Fitting time series models to nonstationary processes," Ann. Statist., vol. 25, pp. 1-37, 1997.
17. M. H. Neumann and R. von Sachs, "Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra," Ann. Statist., vol. 25, pp. 38-76, 1997.
18. M. B. Priestley, Spectral Analysis and Time Series. Boston: Academic, 1981.
19. W. Martin and P. Flandrin, "Wigner-Ville spectral analysis of nonstationary processes," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 1461-1470, 1985.
20. K. S. Riedel, "Optimal data-based kernel estimation of evolutionary spectra," IEEE Trans. Signal Process., vol. 41, pp. 2439-2447, July 1993.