Compressive sensing and random filtering of EEG signals using Slepian basis

Electroencephalography (EEG) is a major tool for clinical diagnosis of neurological diseases and brain research. EEGs are often collected over numerous channels and trials, providing large data sets that require efficient collection and accurate compression. Compressive sensing and random filtering-emphasizing signal “sparseness”- enable the reconstruction of signals from a small set of measurements, at the expense of computationally complex reconstruction algorithms. In this paper we show that using Slepian functions, rather than sinc functions, in sampling reduces the minimum Nyquist sampling rate without aliasing. Assuming non-uniform sampling our procedure can be connected with compressive sensing and random filtering. EEG signals are well projected onto a Slepian basis consisting of finite-support functions, with energy optimally concentrated in a band, and related to the sinc function. Our procedure is illustrated using subdural EEG signals, with better performance than that from the conventional compressive sensing and random filtering, without the complex reconstruction of those methods.