Comparison of a best and a near : best basis approach to wavelet analysis of elctrocardiograms
Date
1996
Authors
Steacy, Robert Clifford Bruce
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Abstract
A necessary first step in the high-speed computerized analysis of electrocardiograms is to transform the data so that as much of the energy of the signal is contained in as few coefficients as possible. This facilitates both de-noising and data compression, so that further steps such as arrhythmia detection can then be carried out.
A logical starting point for electrocardiogram research is provided by the wavelet techniques contained in the standard reference work Numerical Recipes in C, by Press et al. [10]. These are based on the work of Ingrid Daubechies (compactly supported wavelets) and S. Mallat (the pyramid algorithm). Using a well-known measure of the expected information of a signal, this thesis compares the basic treatment of electrocardiograms to two improved schemes, the Near-Best-Basis of Taswell, and the Best Basis of Coifman and Wickerhauser. Mathematical definitions and foundations for "Best" and "Near-Best" are given in Chapter 3 of the thesis.
There are two conclusions. The Near-Best-Basis of Taswell gives a significant improvement over the basic pyramid algorithm treatment for low additional computational cost. The Best Basis produces a further improvement over the Near-Best-Basis which is negligible for practical purposes, and at a large increase in computational cost. These conclusions have valuable practical implications for researchers in this field, and for the estimated several hundred million people worldwide who face serious heart problems in the next decade.