Wavelet Shrinkage Denoising Using the Non-Negative Garrote

In this paper, we combine Donoho and Johnstones Wavelet Shrinkage denoising technique (known as WaveShrink) with Breimans 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 meansquare -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 Steins Unbiased Risk Estimate (SURE) is studied. We also propose a threshold selection procedure based on combining Coifman and Donohos 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 and Phra...