## Multiple Shrinkage and Subset Selection in Wavelets (1997)

Citations: | 127 - 16 self |

### BibTeX

@MISC{Clyde97multipleshrinkage,

author = {Merlise Clyde and Giovanni Parmigiani and Brani Vidakovic},

title = {Multiple Shrinkage and Subset Selection in Wavelets},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper discusses Bayesian methods for multiple shrinkage estimation in wavelets. Wavelets are used in applications for data denoising, via shrinkage of the coefficients towards zero, and for data compression, by shrinkage and setting small coefficients to zero. We approach wavelet shrinkage by using Bayesian hierarchical models, assigning a positive prior probability to the wavelet coefficients being zero. The resulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear shrinkage patterns. We discuss fast computational implementations, with a focus on easy-to-compute analytic approximations as well as importance sampling and Markov chain Monte Carlo methods. Multiple shrinkage estimators prove to have excellent mean squared error performance in reconstructing standard test functions. We demonstrate this in simulated test examples, comparing various implementations of multiple shrinkage to commonly used shrinkage rules. Finally, we illustrate our approach with an application to the so-called "glint" data.

### Citations

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Citation Context ...on in time and scale (frequency), and fast implementation. In statistics, interest in wavelets initiated when Daubechies and Mallat connected wavelets with discrete data processing (Daubechies, 1988; =-=Mallat, 1989-=-), and when Donoho and Johnstone showed that wavelet shrinkage has desirable statistical optimality properties in problems concerning elimination of noise (Donoho et al., 1995). Since then, wavelet re... |

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