Smoothing and Robust Wavelet Analysis
A. Gregory Bruce, David L. Donoho, Hong‐Ye Gao, R. Douglas Martin · COMPSTAT · 1994
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 transforms, 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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.