Proceedings ArticleDOI
Denoising and Robust Non-Linear Wavelet Analysis,
Andrew G. Bruce,David L. Donoho,Hong-Ye Gao,R. D. Martin +3 more
- Vol. 2242, pp 325-336
TLDR
In this paper, the authors developed outlier resistant wavelet transforms, in which outliers and outlier patches are localized to just a few scales, and improved upon the Donoho and Johnstone nonlinear signal extraction methods.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.read more
Citations
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Book
Wavelet Methods for Time Series Analysis
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Multiscale analysis and modeling using wavelets
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References
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Journal ArticleDOI
Adapting to Unknown Smoothness via Wavelet Shrinkage
TL;DR: In this article, the authors proposed a smoothness adaptive thresholding procedure, called SureShrink, which is adaptive to the Stein unbiased estimate of risk (sure) for threshold estimates and is near minimax simultaneously over a whole interval of the Besov scale; the size of this interval depends on the choice of mother wavelet.
Journal ArticleDOI
Singularity detection and processing with wavelets
Stéphane Mallat,Wen-Liang Hwang +1 more
TL;DR: It is proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents.
Journal ArticleDOI
Image compression through wavelet transform coding
TL;DR: If pictures can be characterized by their membership in the smoothness classes considered, then wavelet-based methods are near-optimal within a larger class of stable transform-based, nonlinear methods of image compression.
Journal ArticleDOI
Estimation of time series parameters in the presence of outliers
TL;DR: An iterative procedure is proposed for detecting IO and AO in practice and for estimating the time series parameters in autoregressive-integrated-moving-average models in the presence of outliers.
Journal ArticleDOI
Robust bayesian estimation for the linear model and robustifying the Kalman filter
C. Masreliez,R. Martin +1 more
TL;DR: In this article, robust Bayesian estimates of the vector x are constructed for the following two distinct situations: (1) the state x is Gaussian and the observation error v is (heavy-tailed) non-Gaussian and (2) the states x and v are Gaussian.