Rapid Extraction, Based On Fourth-order Cumulants And Wavelet Transform Of The Brain Evoked Potentials

The evoked potentials (EPs) are bioelectrical signals generated by the central nervous system. The EPs contain a lot of useful signals related to the nervous system, so the EPs have widely clinical application. Less time extraction or even single extraction of the EPs is the focus of the researchers. There are some new methods presented in recent years. They're wavelet transform, higher order correlations, neural networks, independent component analysis and et al. With the development of the modern signal processing technology, several technologies will combine with each other to extract the EPs. This paper combined the wavelet transform with the higher order correlations to extract the EPs. The following is the main study of this paper.(1)We designed an adaptive filter based on the fourth order correlations (FOC). Gradually, the higher order statistics (HOS) become the research hotspot in recent years. One property of the HOS is that all correlations, whose order is above 2, of the Gaussian noise (white or color) are zero. So we designed an adaptive filter based on the fourth order correlations. The impulse response of this filter is estimated by the one dimensional diagonal slice of the fourth order correlations. When observed signal is filtered by this filter, not only the Gaussian noise can be eliminated largely, but also the noise free EPs can be enhanced. It's good for further processing and analysis.(2)We proposed a new wavelet threshold function contraposed the disadvantages of the traditional wavelet de-noising methods. The goal of this research is to extract the EPs quickly. Through the comparison of several traditional wavelet de-noising methods, we knew that the speed of the wavelet threshold de-noising method is quick. The soft threshold function presented by Donoho has a good smoothing property. But there's a stated error between the estimated value and the original data, and the estimated value is less than the original data. Moreover, some useful information may be eliminated by its smoothing property. These shortcomings will affect the exactitude of the reconstructed signal. The hard threshold function can keep the characteristics property. But it's discontinuous in the threshold spot. This will bring concussion to the reconstruct signal. The improved threshold function is continuous like the soft threshold function, and its asymptote is the curve of the hard threshold function. It don't have the stated error like the soft threshold function and have the advantage of keeping character like the hard threshold function. When used in the extraction of the EPs, there will be a better result.(3)Combine the fourth-order-correlation-based filter with the improved wavelet threshold function. When the observed noisy EPs are filtered by the presented filter, most of the background noise is eliminated and the EPs are enhanced. But there are still non-Gaussian noise and residual Gaussian noise. The signal should be processed further more. So we used the improved wavelet threshold function for further process. From several experiments and the comparison with soft and hard threshold functions, we got that, the new method which is a combination of the filter based on the fourth order correlation and the improved wavelet threshold function can extract the EPs quickly and exactly.