Weighted averaging of evoked potentials

Abstract

Weighted averages of brain evoked potentials (EP's) are obtained by weighting each single EP sweep prior to averaging. These weights are shown to maximize the signal-to-noise ratio (SNR) of the resulting average if they satisfy a generalized eigenvalue problem involving the correlation matrices of the underlying signal and noise components. The signal and noise correlation matrices are difficult to estimate and the solution of the generalized eigenvalue problem is often computationally impractical for real-time processing. Correspondingly, a number of simplifying assumptions about the signal and noise correlation matrices are made which allow an efficient method of approximating the maximum SNR weights. Experimental results are given using actual auditory EP data which demonstrate that the resulting weighted average has estimated SNR's that are up to 21% greater than the conventional ensemble average SNR.

Trimmed estimators for robust averaging of event-related potentials

“…It is commonly assumed (e.g., Davila and Mobin (1992)) that signal is contained in the poststimulus part of the averaged data, while noise is included in both poststimulus and prestimulus part. Prestimulus variance usually was much lower than poststimulus variance in our data, thus the impact of noise variance to poststimulus interval was insignificant and we considered the poststimulus part (approximately) as "signal".…”

“…The parameter to be optimized should be chosen carefully according to the objectives of the specific study (note that different approaches to estimation of SNR in ERP exist; see, e.g., Hoke et al (1984); Coppola et al (1978);Davila and Mobin (1992); Özdamar and Delgado (1996)). For unbiased optimization, a separate set of data with characteristics similar to the analyzed data should be used.…”

“…In this method, each epoch is given a weight depending on estimated noise in this epoch (Hoke et al, 1984;Lütkenhöner et al, 1985;Davila and Mobin, 1992;Lȩski, 2002). Though quite many variations of weighting averaging have been developed (for review see, e.g., Lȩski (2002)), this method is still rarely used for averaging of ERP.…”

Accuracy of averaged auditory brainstem response amplitude and latency estimates

“…In contrast, the noise is changed on a trial by trial basis. Using the matrix notation given in (Silva 2009) and (Davila and Mobin 1992), the ensemble of all trial data can be rewritten as:…”

Methods of Weighted Averaging with Application to Biomedical Signals

“…Methods of averaging help in detecting very low amplitude waves (which are called late potentials) originating in the ventricles of abnormal heart conditions patients (Laciar & Jane, 2001). Signal averaging methods are also required in the case of evoked potentials (EP), the electrical potentials recorded from the nervous system of patients, which are effects of a stimulation (in contrast to the spontaneous potentials as in the case of electroencephalography (EEG) or electromyography (EMG)) (Davila, 1992). Traditional arithmetic averaging technique can be used when the noise is stationary (it is constant level of power noise) throughout the averaging period.…”