Wavelet shrinkage denoising using the non-negative garrote

In this article, we combine Donoho and Johnstone's wavelet shrinkage denois ing technique (known as WaveShrink) with Breiman's non-negative garrote. We show that the non-negative garrote shrinkage estimate enjoys the same asym ptotic convergence rate as the hard and the soft shrinkage estimates. Simul ations are used to demonstrate that garrote shrinkage offers advantages ove r both hard shrinkage (generally smaller mean-square-error and less sensiti vity to small perturbations in the data) and soft shrinkage (generally smal ler bias and overall mean-square-error). The minimax thresholds for the non -negative garrote are derived and the threshold selection procedure based o n Stein's unbiased risk estimate (SURE) is studied. We also propose a thres hold selection procedure based on combining Coifman and Donoho's cycle-spin ning and SURE. The procedure is called SPINSURE. We use examples to show th at SPINSURE is more stable than SURE: smaller standard deviation and smalle r range.