Modified Empirical Mode Decomposition to process EEG signal including artefacts

The continuous EEG signal is considered non-stationary. Therefore it is necessary to use time-frequency domain methods to process the EEG signal. One of such methods is Hilbert-Huang transform (HHT). HHT transform was designed especially for processing non-stationary signals. The first part of HHT is the Empirical Mode Decomposition (EMD), which decomposes the signal into Intrinsic Mode Functions (IMFs) defined by the signal itself.

During the EMD we locate local extrema (maxima and minima) and interpolate a cubic spline running between them, so we can get the upper and lower envelope. But when we need to create the complete envelope to cover the whole signal, we have to add additional extremum points, because detected extrema don’t cover the beginning and the end of the signal. Mirror method and Slope-based method in were designed to deal with this task. But these methods don’t reflect specifics of the EEG signal, such as artefacts (significant change of amplitude and frequency). When the artefact is located near the beginning or the end of the signal, then the estimated additional extrema don’t fit to the trend of the signal.

I have proposed two methods, which estimate additional extrema to create complete envelopes. The first method includes first and last sample of the signal to the sets of minima and maxima. The second one is based on the Mirror method. It calculates new extrema prior the first sample/past the last sample of the signal as the mirror images of the first two extrema symmetric to the first/last sample of the signal. If the first estimated extremum is a minimum, we have to ensure, that its value isn’t greater than the value of first sample. If the value of the minimum is greater, then we replace the minimum value with the first sample.

With these two methods the EEG signal could be processed without previous artefact rejection. But there is significant difference between the modified mirror method and the first-last method. Modified mirror method is approximately six times faster than the first-last method. It means that the number of modified mirror method iterations during the sifting process (part of EMD) is six times smaller.