Threshold Selection in WaveShrink

Donoho and Johnstone's wavelet shrinkage denoising technique (known as WaveShrink) consists three steps: (1) transform data into wavelet domain; (2) shrink the wavelet coefficients; and (3) transform the shrunk coefficients back. The choice of shrinkage function and thresholds in step (2) plays an important role for WaveShrink both theoretically and in practice. In this paper, we discuss the issue of threshold selection in WaveShrink. We first review the threshold selection procedure based minimax thresholds and Stein's Unbiased Risk Estimate (SURE). We then propose a new threshold selection procedure based on combining Coifman and Donoho's cycle-spinning and SURE. We call our new procedure SPINSURE. We use examples to show that SPINSURE is numerically more stable than SURE: smaller standard deviation and smaller range. Various comparisons with the ideal and minimax thresholds are also presented. Key Words and Phrases: Cycle-Spinning; Minimax Threshold; Non-negative Garrote; Nonparamet..