De-Noising By Soft-Thresholding

De-Noising By Soft-Thresholding (1992)

by David L. Donoho

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Datum	Value	Source
TITLE	De-Noising By Soft-Thresholding	user correction
AUTHOR NAME	David L. Donoho	user correction
AUTHOR AFFIL	Department of Statistics; Stanford University	user correction
ABSTRACT	Donoho and Johnstone (1992a) proposed a method for reconstructing an unknown function f on [0; 1] from noisy data di = f(ti)+ zi, iid i =0;:::;n 1, ti = i=n, zi N(0; 1). The reconstruction fn ^ is de ned in the wavelet domain by translating all the empirical wavelet coe cients of d towards 0 by an amount p 2 log(n) = p n. We prove two results about that estimator. [Smooth]: With high probability ^ fn is at least as smooth as f, in any of a wide variety of smoothness measures. [Adapt]: The estimator comes nearly as close in mean square to f as any measurable estimator can come, uniformly over balls in each of two broad scales of smoothness classes. These two properties are unprecedented in several ways. Our proof of these results develops new facts about abstract statistical inference and its connection with an optimal recovery model.	user correction
YEAR	1992	user correction
CITATIONS	39 found	ParsCit 1.0