Journal Article

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

Cressie, N., Huang, H.-C.

2000

Overview

In a series of recent articles on nonparametric regression, Donoho and Johnstone developed waveletshrinkage methods for recovering unknown piecewise-smooth deterministic signals from noisy data. Wavelet shrinkage based on the Bayesian approach involves specifying a prior distribution on the wavelet coefficients, which is usually assumed to have a distribution with zero mean. There is no a priori reason why all prior means should be 0; indeed, one can imagine certain types of signals in which this is not a good choice of model. In this article, we take an empirical Bayes approach in which we propose an estimator for the prior mean that is \"plugged into\" the Bayesian shrinkage formulas. Another way we are more general than previous work is that we assume that the underlying signal is composed of a piecewise-smooth deterministic part plus a zero-mean stochastic part; that is, the signal may contain a reasonably large number of nonzero wavelet coefficients. Our goal is to predict this signal from noisy data. We also develop a new estimator for the noise variance based on a geostatistical method that considers the behavior of the variogram near the origin. Simulation studies show that our method (DecompShrink) outperforms the wellknown VisuShrink and SureShrink methods for recovering a wide variety of signals. Moreover, it is insensitive to the choice of the lowest-scale cut-off parameter, which is typically not the case for other wavelet-shrinkage methods.

• Publisher: Taylor & Francis Group,The American Society for Quality and The American Statistical Association,American Society for Quality Control,American Statistical Association,American Society for Quality
• Subject: Covariance / Determinism / EM algorithm / Empirical Bayes / Estimation methods / Estimators / Exact sciences and technology / Image denoising / Image reconstruction / Linear inference, regression / Mathematical foundations / Mathematics / Maximum likelihood estimation / Multiscale graphical model / Multiscale modeling / Nonparametric inference / Nonparametric regression / Normal probability plot / Probability and statistics / Sciences and techniques of general use / Signal noise / Statistics / Threshing / Wavelet analysis