Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Student- t distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R- SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.Comment: Under Review by IEEE Transactions on Signal Processin

Extraction of vocal-tract system characteristics from speechsignals

We propose methods to track natural variations in the characteristics of the vocal-tract system from speech signals. We are especially interested in the cases where these characteristics vary over time, as happens in dynamic sounds such as consonant-vowel transitions. We show that the selection of appropriate analysis segments is crucial in these methods, and we propose a selection based on estimated instants of significant excitation. These instants are obtained by a method based on the average group-delay property of minimum-phase signals. In voiced speech, they correspond to the instants of glottal closure. The vocal-tract system is characterized by its formant parameters, which are extracted from the analysis segments. Because the segments are always at the same relative position in each pitch period, in voiced speech the extracted formants are consistent across successive pitch periods. We demonstrate the results of the analysis for several difficult cases of speech signals