Statistical method for sparse coding of speech including a linear predictive model

Recently, different methods for obtaining sparse representations of a signal using dictionaries of waveforms have been studied. They are often motivated by the way the brain seems to process certain sensory signals. Algorithms have been developed using a specific criterion to choose the waveforms occurring in the representation. The waveforms are choosen from a fixed dictionary and some algorithms also construct them as a part of the method. In the case of speech signals, most approaches do not take into consideration the important temporal correlations that are exhibited. It is known that these correlations are well approximated by linear models. Incorporating this a priori knowledge of the signal can facilitate the search for a suitable representation solution and also can help with its interpretation. Lewicki proposed a method to solve the noisy and overcomplete independent component analysis problem. In the present paper we propose a modification of this statistical technique for obtaining a sparse representation using a generative parametric model. The representations obtained with the method proposed here and other techniques are applied to artificial data and real speech signals, and compared using different coding costs and sparsity measures. The results show that the proposed method achieves more efficient representations of these signals compared to the others. A qualitative analysis of these results is also presented, which suggests that the restriction imposed by the parametric model is helpful in discovering meaningful characteristics of the signals.