Wavelet Shrinkage Denoising Using the Non-Negative Garrote

Abstract

In this article, we combine Donoho and Johnstone's wavelet shrinkage denoising technique (known as WaveShrink) with Breiman's non-negative garrote. We show that the non-negative garrote shrinkage estimate enjoys the same asymptotic convergence rate as the hard and the soft shrinkage estimates. Simulations are used to demonstrate that garrote shrinkage offers advantages over both hard shrinkage (generally smaller mean-square-error and less sensitivity to small perturbations in the data) and soft shrinkage (generally smaller bias and overall mean-square-error). The minimax thresholds for the non-negative garrote are derived and the threshold selection procedure based on Stein's unbiased risk estimate (SURE) is studied. We also propose a threshold selection procedure based on combining Coifman and Donoho's cycle-spinning and SURE. The procedure is called SPINSURE. We use examples to show that SPINSURE is more stable than SURE: smaller standard deviation and smaller range.

Key Words:

• Cycle-spinning
• Minimax threshold
• Nonparametric regression
• Shrinkage functions
• Stein's unbiased risk estimate (SURE)
• WaveShrink