Wavelet Estimation of a Baseline Signal From Repeated Noisy Measurements by Vertical Block Shrinkage

Abstract

In this paper a new wavelet shrinkage technique is proposed and investigated. When data consist of a multiplicity of related noisy signals, we propose a wavelet-based shrinkage estimation procedure to summarize all data components into a single regularized and representative signal ("base-line"). This fusion of information from different runs is done via Stein-type shrinkage rule resulting from an empirical Bayes argument. The proposed shrinkage estimators maximize the predictive density under appropriate model assumptions on the wavelet coefficients. Features of this model-induced shrinkage are that it is "block-vertical" and local in time. The method, called VERTISHRINK, is evaluated on a battery of test signals under various signal-to-noise ratios and various number of vector components. An application in estimating the base-line signal in an experiment in tumor physiology is provided as well.