Denoising and robust nonlinear wavelet analysis

Andrew G. Bruce; David L. Donoho; Hong-Ye Gao; R. Douglas Martin

doi:10.1117/12.170036

15 March 1994 Denoising and robust nonlinear wavelet analysis

Andrew G. Bruce, David L. Donoho, Hong-Ye Gao, R. Douglas Martin

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170036
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

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.

Citation Download Citation

Andrew G. Bruce, David L. Donoho, Hong-Ye Gao, and R. Douglas Martin "Denoising and robust nonlinear wavelet analysis", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170036

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