Stochastic Gabor dictionaries

For a time-frequency parametrization, we construct the dictionary D from Gabor functions (sine modulated gaussians), which offer the lowest product of joint time-frequency spread (each dictionary contains also complete Fourier and Dirac bases). But the number of Gabor functions, which can be fitted to a given signal, is a priori infinite. Therefore in practice we restrict the dictionary D to a subset, obtained by subsampling the space of possible parameters of Gabor functions. For example, in [9] and [8] a dyadic (wavelet-like) scheme of subsampling was used. Analyzing large amounts of sleep EEG, we encountered a statistical bias of MP decomposition, resulting from the fixed structure of the dictionary used in [8]. Since any fixed structure of a dictionary will introduce a statistical bias in the resulting MP decomposition, as a bias-free solution we proposed stochastic dictionaries [3], where the parameters of dictionary's waveforms are drawn from flat distributions.