ASA 125th Meeting Ottawa 1993 May

1pNS4. Nonlinear and robust signal extraction based on wavelets.

Andrew G. Bruce

Statistical Sciences, Inc., 1700 Westlake Ave. N., Seattle, WA 98109

David L. Donoho

Stanford Univ., Stanford, CA 94305

R. Douglas Martin

Statistical Sciences, Inc., Seattle, WA 98109

The wavelet transform is an important new tool in applied mathematics, engineering, and science. In a series of papers, Donoho and Johnstone (1992) develop a powerful theory based on wavelets for extracting nonsmooth signals from noisy data. Several nonlinear smoothing algorithms are presented that provide high performance for a wide range of spatially inhomogeneous signals. These algorithms are computationally very fast. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to outliers in the data. The effect of a large isolated observation on the wavelet transform is smeared through all wavelet scales. In this paper, outlier resistant wavelet transforms are developed. In these transforms, outliers and outlier patches are localized to just a few scales. Hence, it is easy to identify and remove the outliers. By using the outlier resistant wavelet transforms, the Donoho and Johnstone nonlinear signal extraction methods are improved upon. These algorithms prevent outliers from leaking into the extracted signal. Applications will be given for a variety of data sets, including ocean acoustic data (e.g., ice cracking) and glint noise. [This research is supported by ONR Contract No. N00014-92-C-0066.] [sup a)]Also with Department of Statistics, University of Washington, Seattle, WA 98195.