Experiments in Wavelet Shrinkage Denoising

Abstract

Previous simulation experiments for the comparison of wavelet shrinkage denoising methods have failed to demonstrate significant differences between methods. Such differences have never been clearly demonstrated due to the use of qualitative comparisons or of quantitative comparisons that suffered from insufficient sample size and/or absent confidence intervals for the figure of merit investigated.

In particular, previous studies have used lion-robust measures as figures of merit for fixed signal classes defined by adding instances of noise to the same instance of the fixed test signal. New simulation experiments are reported here that instead use robust measures for randomized signal classes defined by adding instances of noise to different instances of randomized test signals.

Significantly greater variability in the performance of the denoising methods was observed when comparing results obtained with randomized rather than fixed signal classes. However, the use of robust measures does facilitate statistically valid comparisons with respect to this variability. Indeed, the use of non-robust or of non-randomized signal classes can result in misleading inferences from invalid comparisons. Thus, the combined use of both should yield more realistic and meaningful simulation results that better represent the real-world context intended for applied use of the denoising methods.