Neuromodulations are an important component of extracellular electrical potentials (EEP), such as the Electroencephalogram (EEG), Electrocorticogram (ECoG) and Local Field Potentials (LFP). This spatially temporal organized multi-frequency transient (phasic) activity reflects the multiscale spatiotemporal synchronization of neuronal populations in response to external stimuli or internal physiological processes. We propose a novel generative statistical model of a single EEP channel, where the collected signal is regarded as the noisy addition of reoccurring, multi-frequency phasic events over time. One of the main advantages of the proposed framework is the exceptional temporal resolution in the time location of the EEP phasic events, e.g., up to the sampling period utilized in the data collection. Therefore, this allows for the first time a description of neuromodulation in EEPs as a Marked Point Process (MPP), represented by their amplitude, center frequency, duration, and time of occurrence. The generative model for the multi-frequency phasic events exploits sparseness and involves a shift-invariant implementation of the clustering technique known as k-means. The cost function incorporates a robust estimation component based on correntropy to mitigate the outliers caused by the inherent noise in the EEP. Lastly, the background EEP activity is explicitly modeled as the non-sparse component of the collected signal to further improve the delineation of the multi-frequency phasic events in time. The framework is validated using two publicly available datasets: the DREAMS sleep spindles database and one of the Brain-Computer Interface (BCI) competition datasets. The results achieve benchmark performance and provide novel quantitative descriptions based on power, event rates and timing in order to assess behavioral correlates beyond the classical power spectrum-based analysis. This opens the possibility for a unifying point process framework of multiscale brain activity where simultaneous recordings of EEP and the underlying single neuron spike activity can be integrated and regarded as marked and simple point processes, respectively.
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