WaveShrink: shrinkage functions and thresholds

Andrew G. Bruce; Hong-Ye Gao

doi:10.1117/12.217582

1 September 1995 WaveShrink: shrinkage functions and thresholds

Andrew G. Bruce, Hong-Ye Gao

Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217582
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Donoho and Johnstone's WaveShrink procedure has proven valuable for signal de-noising and non-parametric regression. WaveShrink is based on the principle of shrinking wavelet coefficients towards zero to remove noise. WaveShrink has very broad asymptotic near- optimality properties. In this paper, we introduce a new shrinkage scheme, semisoft, which generalizes hard and soft shrinkage. We study the properties of the shrinkage functions, and demonstrate that semisoft shrinkage offers advantages over both hard shrinkage (uniformly smaller risk and less sensitivity to small perturbations in the data) and soft shrinkage (smaller bias and overall L₂ risk). We also construct approximate pointwise confidence intervals for WaveShrink and address the problem of threshold selection.

Citation Download Citation

Andrew G. Bruce and Hong-Ye Gao "WaveShrink: shrinkage functions and thresholds", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217582

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