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Abstract: Suppose we have observations y i = s i +z i , i = 1; :::; n, where (s i ) is signal and (z i ) is i.i.d. Gaussian white noise. Suppose we have available a library L of orthogonal bases, such as the Wavelet Packet bases or the Cosine Packet bases of Coifman and Meyer. We wish to select, adaptively based on the noisy data (y i ), a basis in which best to recover the signal ("de-noising"). Let M n be the total number of distinct vectors occcuring among all bases in the library and let t n = p 2... (Update)
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19: Orthonormal bases of compactly supported wavelets (context) - Daubechies - 1988
18: Entropybased algorithms for best basis selection - Coifman, Wickerhauser - 1992
17: noising by soft-thresholding - Donoho - 1994
BibTeX entry: (Update)
Donoho, D. L. and Johnstone, I. M. (1994c). Ideal Denoising in an orthonormal basis chosen from a library of bases, C. R. Acad. Sci. Paris, Ser. I, 319, 000-000 (in press). http://citeseer.ist.psu.edu/7496.html More
@techreport{ donoho94ideal,
author = "D. L. Donoho and I. M. Johnstone",
title = "Ideal Denoising in an Orthonormal Basis Chosen from a Library of Bases",
year = "1994",
url = "citeseer.ist.psu.edu/7496.html" }
Citations (may not include all citations):360 Entropy-based algorithms for best-basis selection - Coifman, Wickerhauser - 1992
243 Ideal Spatial Adaptation via Wavelet Shrinkage (context) - Donoho, Johnstone
198 Wavelet Shrinkage: Asymptopia - Donoho, Johnstone et al.
129 Probability in Banach Spaces (context) - Talagrand, Ledoux
108 Unconditional bases are optimal bases for data compression a.. - Donoho - 1993
50 Simultaneous Noise Suppression and Signal Compression using .. - Saito
45 Wavelet analysis and signal processing - Coifman, Meyer et al. - 1992
44 Nonlinear Wavelet Methods for Recovery of Signals (context) - Donoho - 1993
41 Remarques sur l'analyse de Fourier `a fenetre (context) - Coifman, Meyer - 1991
23 Rates of Convergence of Minimum Contrast Estimators (context) - Birg'e, Massart - 1993
19 Fast wavelet techniques for near-optimal image processing - DeVore, Lucier - 1992
18 Estimation d'une densit'e de probabilit'e par m'ethode d'ond.. (context) - Johnstone, Kerkyacharian et al. - 1992
12 Ideal Time-Frequency Denoising (context) - Donoho, Johnstone
10 Rate of convergence of nonparametric estimates of maximum-li.. (context) - Nemirovskii, Polyak et al. - 1985
8 A new approach to least-squares estimation (context) - Geer - 1988
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