Methods of Weighted Averaging with Application to Biomedical Signals

During the analysis of real biomedical signals it can almost always be seen noise that distorts the image. The presence of interference is associated with the specific acquisition of these signals. For example in the case of bioelectric signals, disturbances may come from the hardware retrieves those signals, the powerline or the bioelectric activity of body cells. The bioelectric signals, which are widely used in most fields of biomedicine, are generated by nerve cells or muscle cells. The electric field propagates through the tissue and can be acquired from the body surface, eliminating the potential need to invade the biosystem. However, using surface electrodes results in high amplitude of noise and the noise should be suppressed to extract a priori desired information (Bruce, 2001). There are many approaches to the noise reduction problem while preserving the variability of the desired signal morphology. One of the possible methods of noise attenuation is low-pass filtering such as arithmetic mean. The classical band-pass filtering is very simple method but also very ineffective because the frequency characteristics of signal and noise significantly overlap. Therefore there are developed other methods of noise attenuation based on transforming the input space of signal and creating a new space with the help of discrete cosine transform (Paul et al., 2000) or wavelets transform (Augustyniak, 2006), based on fuzzy nonlinear regression (Momot et al., 2005), nonlinear projective filtering (Kotas, 2009), higher-order statistics at different wavelet bands (Sharma et al., 2010) or extreme points determination by mean shift algorithm and dynamical model-based nonlinear filtering (Yan et al., 2010). In the case of repeatable biomedical signals, another possible method of noise attenuation is the synchronized averaging (Jane et al., 1991). The method assumes that the biomedical signal is quasi-cyclic and the noise is additive, independent and with zero mean. Averaging could be performed by simple arithmetic mean or its generalization, namely weighted mean where the weights are tuned by some adaptive algorithm. Recently there have been published several works concerning different approaches to the problem of determining the weights. The algorithm of adaptive estimation of the weights is described in (Bataillou et al., 1995). In (Leski, 2002) there is described method of estimation of the weights based on criterion function minimization. Application of Bayesian inference to the weights estimation problem is presented in (Momot et al., 2007a) and (Momot, 2008b). Weighted averaging method based on partition of input data set in time domain is described in (Momot et al, 2007b). The generalization of the method is presented in (Momot, 16