Figure 13

Statistical properties of MP decomposition of 50 epochs of sleep EEG (a, b) and white noise (c-f) over dyadic (a, c, e) and stochastic (b, d, f) dictionaries. Histograms of frequency centers of atoms fitted by MP decomposition over dyadic dictionary to EEG (a) and noise (c) reveal additional structure, absent in corresponding decompositions performed over stochastic dictionaries b and d, respectively. Maximum in the middle of frequency range in panel d results from convention of assigning half of Nyquist frequency to Dirac's delta. In the top panel centers of atoms fitted to white noise are given in the time-frequency plane for dyadic (left, e) and stochastic (right, f) dictionaries