MULTIPLE SHRINKAGE AND SUBSET-SELECTION IN WAVELETS

This paper discusses Bayesian methods for multiple shrinkage estimatio n in wavelets. Wavelets are used in applications for data denoising, v ia shrinkage of the coefficients towards zero, and for data compressio n, by shrinkage and setting small coefficients to zero. We approach wa velet shrinkage by using Bayesian hierarchical models, assigning a pos itive prior probability to the wavelet coefficients being zero. The re sulting estimator for the wavelet coefficients is a multiple shrinkage estimator that exhibits a wide variety of nonlinear patterns. We disc uss fast computational implementations, with a focus on easy-to-comput e analytic approximations as well as importance sampling and Markov ch ain Monte Carlo methods. Multiple shrinkage estimators prove to have e xcellent mean squared error performance in reconstructing standard tes t functions. We demonstrate this in simulated test examples, comparing various implementations of multiple shrinkage to commonly-used shrink age rules. Finally, we illustrate our approach with an application to the so-called 'glint' data.