Extraction of weak bioelectrical signals by means of singular value decomposition
Most measurements of human electrical activity contain large amounts of electrical heart activity (electrocardiogram, ECG). Whenever other sources of lower energy are of interest, a need arises to eliminate this ECG. Some applications allow a frequency domain operation (e.g. gastro-intestinal slow wave detection), or even a time domain operation (e.g. blanking of QRS complex of an ECG). Usually none of these methods are adequate. The proposed method uses a totally different approach, in this sense that it manipulates geometrically all measurements at the same time. It decomposes the measurements on the basis of an oriented energy, by means of the singular value decomposition. After an introduction to the problem and a definition of some useful concepts, the basic idea of the method is presented in a low dimensional geometrical example, and generalized to higher dimensions. It is shown that the method can easily be applied under realistic clinical conditions. A discussion is given about : the influence of noise; considerations on correlations between source signals; number and location of electrodes; certain dynamical problems like interference. Results on real data are given, in order to illustrate and verify the main features of the method : the multidimensional approach to the estimation of equivalent dipole vector sources; the insensitivity of ECG elimination quality to actual electrode positions; the minimal rank representation of the source signals and the resulting signal to noise ratio improvement; 50 Hz or 60 Hz interference elimination.
KeywordsSingular Value Decomposition Source Signal Source Vector Weak Source Dipole Vector
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