Abstract
Electroencephalograms (EEGs) measure a brain signal that contains abundant information about the human brain function and health. For this reason, recent clinical brain research and brain computer interface (BCI) studies use EEG signals in many applications. Due to the significant noise in EEG traces, signal processing to enhance the signal to noise power ratio (SNR) is necessary for EEG analysis, especially for non-invasive EEG. A typical method to improve the SNR is averaging many trials of event related potential (ERP) signal that represents a brain’s response to a particular stimulus or a task. The averaging, however, is very sensitive to variable delays. In this study, we propose two time delay estimation (TDE) schemes based on a joint maximum likelihood (ML) criterion to compensate the uncertain delays which may be different in each trial. We evaluate the performance for different types of signals such as random, deterministic, and real EEG signals. The results show that the proposed schemes provide better performance than other conventional schemes employing averaged signal as a reference, e.g., up to 4 dB gain at the expected delay error of 10°.
Highlights
Electroencephalograms (EEGs) measure electrical brain activity using various EEG sensors, i.e., dry type electrodes [1,2] and hydrogel based electrodes [3]
A typical method to enhance the signal to noise power ratio (SNR) is by measuring many trials of event-related potential (ERP) signals that represent a brain’s response to a particular stimulus or a task and averaging the trials to obtain ERP data with less noise
Averaging trials reduces noise power, enabling enhancement of the ERP signal SNR. This is based on the fact that ERP has the same signal waveform in the trials if there is no delay error in them, but the background brain activities that are not related to the event are independent in each of the trials
Summary
Electroencephalograms (EEGs) measure electrical brain activity using various EEG sensors, i.e., dry type electrodes [1,2] and hydrogel based electrodes [3]. In order to prevent the performance degradation due to these problems, we propose two TDE schemes based on a joint ML criterion that estimates time delays of all the trial signals simultaneously without ERP signal estimation, applying a time delay set that is a vector composed of all time delays. The optimum TDE requires only an autocorrelation function of the ERP signal which contains the ERP signal covariance information in multiple trials instead of the ERP signal itself, and the sub-optimum TDE can be applied without any ERP signal information such as mean and variance They can obtain this by estimating delay vectors for all trials instead of a single trial time delay estimation.
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