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Proceedings Paper

Denoising and robust nonlinear wavelet analysis
Author(s): Andrew G. Bruce; David L. Donoho; Hong-Ye Gao; R. Douglas Martin
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Paper Abstract

In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.

Paper Details

Date Published: 15 March 1994
PDF: 12 pages
Proc. SPIE 2242, Wavelet Applications, (15 March 1994); doi: 10.1117/12.170036
Show Author Affiliations
Andrew G. Bruce, MathSoft, Inc. (United States)
David L. Donoho, Stanford Univ. (United States)
Hong-Ye Gao, MathSoft, Inc. (United States)
R. Douglas Martin, MathSoft, Inc. (United States)

Published in SPIE Proceedings Vol. 2242:
Wavelet Applications
Harold H. Szu, Editor(s)

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