We propose applying sparse modeling using matching pursuit with a Gabor dictionary of scaled time-frequency atoms to analyze and approximate the heart sound signals of the PhysioNet2016 challenge. The time and frequency resolution of the dictionary is governed by a scaling factor, and the atoms temporally overlap by 50% of their temporal duration. We aim to optimize the time and frequency resolution of the dictionary to achieve the highest approximation quality at the desired sparsity. We also investigate the approximation quality of matching pursuit with a reduced size dictionary constructed from either overlapping or nonoverlapping atoms with downsampled frequency resolution. Experimental analysis shows that a dictionary of balanced time and frequency resolution performs well for highly sparse approximations of the signals. Moreover, the highest approximation quality is obtained when the approximation become less sparse, with a dictionary containing atoms of high time and low frequency resolution. On the other hand, a half-size dictionary of overlapping atoms with downsampled frequency resolution performs well in comparison to the original full-size dictionary. Furthermore, the approximation quality is highly degraded when the dictionary contains nonoverlapping atoms rather than atoms with downsampled frequency resolution.

In Gaussian model-based multichannel audio source separation, the likelihood of observed mixtures of source signals is parametrized by source spectral variances and by associated spatial covariance matrices. These parameters are estimated by maximizing the likelihood through an expectation-maximization algorithm and used to separate the signals by means of multichannel Wiener filtering. We propose to estimate these parameters by applying nonnegative factorization based on prior information on source variances. In the nonnegative factorization, spectral basis matrices can be defined as the prior information. The matrices can be either extracted or indirectly made available through a redundant library that is trained in advance. In a separate step, applying nonnegative tensor factorization, two algorithms are proposed in order to either extract or detect the basis matrices that best represent the power spectra of the source signals in the observed mixtures. The factorization is achieved by minimizing the β-divergence through multiplicative update rules. The sparsity of factorization can be controlled by tuning the value of β. Experiments show that sparsity, rather than the value assigned to β in the training, is crucial in order to increase the separation performance. The proposed method was evaluated in several mixing conditions. It provides better separation quality with respect to other comparable algorithms.

This work proposes a solution to the problem of under-determined audio source separation using pre-trained redundant source-based prior information. In local Gaussian modeling of a mixing process, an observed mixture is modeled by a Gaussian distribution parameterized by source variances and spatial covariance matrices. The separation is performed by estimating the parameters, and applying Wiener filtering on the observed mixture. We propose, in a training phase, to build a redundant library of spectral basis matrices of all probable source power spectra, applying non-negative tensor factorization (NTF). In the testing phase, the matrices that match the observed mixture are detected using NTF. With the help of the detected matrices, a maximum likelihood algorithm is proposed in order to iteratively estimate the parameters of the model, exploiting the spatial redundancy of the observed mixture and using NTF. The proposed algorithm proves more flexibility and efficiency with respect to a baseline algorithm used as a reference.

Multichannel sparse representation of acoustic sources has shown to provide an attractive framework for source separation. The multichannel sparse modeling assumes an ability to describe signals as linear combinations of few atoms from a pre-specified dictionary. The dictionary is built by simulating room impulse responses on a grid of locations, exploiting a prior knowledge on the room geometry and reflection coefficients. However, due to the simplified modeling, any mismatch between the simulated and true observed RIRs would generate a considerable distortion in the recovered output signals. In this work we propose an unsupervised adaptation of the dictionary through a semi-blind weighted Natural Gradient, assuming spatio-temporal source sparseness. The system continuously adapts the atoms with the incoming data, improving the match between the dictionary and the true mixing parameters. Results over simulated data show that the proposed framework is a promising solution to underdetermined convolutive source separation in difficult acoustic scenarios.