Two-Stage Atomic Decomposition of Multichannel EEG and the Previously Undetectable Sleep Spindles

We propose a two-step procedure for atomic decomposition of multichannel EEGs, based upon multivariate matching pursuit and dipolar inverse solution, from which atoms representing relevant EEG structures are selected according to prior knowledge. We detect sleep spindles in 147 polysomnographic recordings from the Montreal Archive of Sleep Studies. Detection is compared with human scorers and two state-of-the-art algorithms, which find only about a third of the structures conforming to the definition of sleep spindles and detected by the proposed method. We provide arguments supporting the thesis that the previously undetectable sleep spindles share the same properties as those marked by human experts and previously applied methods, and were previously omitted only because of unfavorable local signal-to-noise ratios, obscuring their visibility to both human experts and algorithms replicating their markings. All detected EEG structures are automatically parametrized by their time and frequency centers, width duration, phase, and spatial location of an equivalent dipolar source within the brain. It allowed us, for the first time, to estimate the spatial gradient of sleep spindles frequencies, which not only confirmed quantitatively the well-known prevalence of higher frequencies in posterior regions, but also revealed a significant gradient in the sagittal plane. The software used in this study is freely available.