Event-Related Potential Noise Reduction Using the Hidden Markov Tree Model

5. Conclusions

In this paper we have modeled a single trial ERP segment using the wavelet-based HMT model as an alternative to the averaging method for ERP analysis. The objective is to capture the dynamic changes of the ERP that the averaging method does not capture by allowing the estimation of the ERP for each single-trial.

The HMT takes advantage of the persistence and clustering characteristics of the wavelet transform to model correlation structures within coefficients across scales, an approach that other wavelet-based methods do not use. These properties are suitable to model the statistical characteristics of an ERP signal. Due to the difficulty of knowing the signal distribution of an ERP segment, the use of a wavelet-based hidden Markov model is an advancement on the simple assumption of the Gaussian independent and identical distributions made by other noise reduction methods. This distribution is approximated using the Gaussian mixture included in the model.

Experimental results with synthetic signals show that the HMT tree model will achieve a measurable improvement in the SNR of the estimate. When used in real ERP signals, the HMT produces estimates which preserve many of the features that are apparent in the noisy signal. In contrast, another wavelet-based method, the soft-thresholding method, appears to be inferior in preserving these features.