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Bivariate hard thresholding in wavelet function estimation (2006)
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BibTeX
@MISC{Fryzlewicz06bivariatehard,
author = {Piotr Fryzlewicz},
title = {Bivariate hard thresholding in wavelet function estimation},
year = {2006}
}
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Abstract
We propose a generic bivariate hard thresholding estimator of the discrete wavelet coefficients of a function contaminated with i.i.d. Gaussian noise. We demonstrate its good risk properties in a motivating example, and derive upper bounds for its mean-square error. Motivated by the clustering of large wavelet coefficients in real-life signals, we propose two wavelet denoising algorithms, both of which use specific instances of our bivariate estimator. The BABTE algorithm uses basis averaging, and the BITUP algorithm uses the coupling of “parents” and “children” in the wavelet coefficient tree. We prove the L2 near-optimality of both algorithms over the usual range of Besov spaces, and demonstrate their excellent finite-sample performance. Finally, we propose a robust and effective technique for choosing the parameters of BITUP in a data-driven way.
Keyphrases
wavelet function estimation bivariate hard thresholding data-driven way effective technique gaussian noise real-life signal excellent finite-sample performance l2 near-optimality large wavelet coefficient mean-square error specific instance good risk property bitup algorithm bivariate estimator babte algorithm generic bivariate wavelet coefficient tree motivating example derive upper bound besov space usual range basis averaging discrete wavelet coefficient
