Separation of transient and oscillatory cereberal activities using over-complete rational dilation wavelt transforms

Many physiological signals such as the electroencephalogram EEG are composed of the superposition of oscillatory activities and transient activities. The oscillatory activities come from rhythmic patterns like delta 0-3 Hz, theta 4-7 Hz, alpha 8-12 Hz, beta 12-30 Hz, gamma 26-100 Hz, and HFOs: High frequency oscillations 80-500Hz. Whereas, the transient activities come from non-rhythmic brain activities like spikes, sharp waves, artifacts, and vertex waves of varying amplitude; shape; and duration. The problem is that the transient activities with different morphologies could overlap in both time and frequency domain with oscillatory patterns, that make the detection a difficult task at present. Visual identification of HFOs which represent an important biomarker of the seizure focus in epileptic patients is extremely tedious and time consuming. For this reason, many algorithms have been recently developed to detect HFOs. However, the developed algorithms suffer from false positives detection resulting from filtered-spikes without HFOs and sharp transients activities. HFOs exist in the frequency ban 80-50Hz and divided into Ripples 80-250 Hz and Fast Ripples 250-500Hz. The transient activities cover a wide bandwith from low to high frequencies and merely resemble HFOs events when filtered using classical band pass filters. However, using classical filtering methods based on FIR filters, wavelet transforms and the matching pursuit cannot separate the oscillatory from transient activities. This paper describes a practical approachof resonance based-filtering for decomposing intracranial EEG recordings of epileptic patients into the sum of an oscillatory component and transient component using over-complete rational dilation wavelet transforms (over complete RADWT) in conjunction with morphological component analysis (MCA).