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Proceedings Paper

WaveShrink: shrinkage functions and thresholds
Author(s): Andrew G. Bruce; Hong-Ye Gao
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Paper Abstract

Donoho and Johnstone's WaveShrink procedure has proven valuable for signal de-noising and non-parametric regression. WaveShrink is based on the principle of shrinking wavelet coefficients towards zero to remove noise. WaveShrink has very broad asymptotic near- optimality properties. In this paper, we introduce a new shrinkage scheme, semisoft, which generalizes hard and soft shrinkage. We study the properties of the shrinkage functions, and demonstrate that semisoft shrinkage offers advantages over both hard shrinkage (uniformly smaller risk and less sensitivity to small perturbations in the data) and soft shrinkage (smaller bias and overall L2 risk). We also construct approximate pointwise confidence intervals for WaveShrink and address the problem of threshold selection.

Paper Details

Date Published: 1 September 1995
PDF: 12 pages
Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); doi: 10.1117/12.217582
Show Author Affiliations
Andrew G. Bruce, MathSoft, Inc. (United States)
Hong-Ye Gao, MathSoft, Inc. (United States)

Published in SPIE Proceedings Vol. 2569:
Wavelet Applications in Signal and Image Processing III
Andrew F. Laine; Michael A. Unser, Editor(s)

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