Preprint #97-23

Deterministic/Stochastic Wavelet Decomposition for Recovery of Signal From Noisy Data

by

Hsin-Cheng Huang and Noel Cressie

In a series of papers on nonparametric regression, D. Donoho and I. Johnstone develop wavelet shrinkage methods for recovering unknown deterministic signals from noisy data. We propose a new approach to wavelet shrinkage in the case where a stochastic signal is present. In particular, we assume that the observed process can be decomposed into deterministic signal plus zero-mean stochastic signal plus noise, a model which is common in spatial statistics and time series. Our goal is still to filter out the noise but the presence of the stochastic part of the signal means that the signal typically does not have a sparse wavelet representation. We also develop a new estimator for the noise parameter based on a geostatistical method that considers the behavior of the variogram near the origin. Simulation studies show that our method (DecompShrink) outperforms the well known VisuShrink and the SureShrink methods for recovering both deterministic and stochastic signals.

Copies of preprints are available from the author upon request. Use the preprint number (located at the top of the page) and make the request directly to the author, Iowa State University, Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.