The electrical activities of neuronal populations in the brain manifest as complex signals that can be recorded as a time series of electric potential differences on the human scalp. An event-related brain potential (ERP) is a peculiar feature in the signals, which is evoked by a specific stimulus or task, the so-called ‘event’. The ERP contains a considerable number of distinct meaningful peak components that reflect brain functions related to the event. The complexity of the ERP can be easily characterized if it can be reliably decomposed into its subcomponents, thereby enabling the localization of the equivalent dipole sources corresponding to those components. To date, this decomposition has typically been performed using independent component analysis (ICA) or principal component analysis (PCA), both of which exploit the statistical independence or uncorrelatedness of sources. However, the temporally overlapped, distinct single-peak-pulse (SPP) signals within a time series are not only mutually dependent but also mutually correlated. In this paper, we propose a gradient descent method for the blind separation of dependent peak signal sources. The method does not exploit any statistical properties of the sources; rather, it uses simple functions characterizing the shapes of the output waveforms and an adaptive peak-searching technique. Application of the proposed method to a numerical example and data from a real ERP experiment suggest that it is superior to an ICA in terms of extracting peak component sources.
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