A fast EM algorithm for Gaussian model-based source separation

International audienceWe consider the FASST framework for audio source separation, which models the sources by full-rank spatial covariance matrices and multilevel nonnegative matrix factorization (NMF) spectra. The computational cost of the expectation-maximization (EM) algorithm in [1] greatly increases with the number of channels. We present alternative EM updates using discrete hidden variables which exhibit a smaller cost. We evaluate the results on mixtures of speech and real-world environmental noise taken from our DEMAND database. The proposed algorithm is several orders of magnitude faster and it provides better separation quality for two-channel mixtures in low input signal-to-noise ratio (iSNR) conditions

Enhanced independent vector analysis for speech separation in room environments

PhD ThesisThe human brain has the ability to focus on a desired sound source in the presence of several active sound sources. The machine based method lags behind in mimicking this particular skill of human beings. In the domain of digital signal processing this problem is termed as the cocktail party problem. This thesis thus aims to further the eld of acoustic source separation in the frequency domain based on exploiting source independence. The main challenge in such frequency domain algorithms is the permutation problem. Independent vector analysis (IVA) is a frequency domain blind source separation algorithm which can theoretically obviate the permutation problem by preserving the dependency structure within each source vector whilst eliminating the dependency between the frequency bins of di erent source vectors. This thesis in particular focuses on improving the separation performance of IVA algorithms which are used for frequency domain acoustic source separation in real room environments. The source prior is crucial to the separation performance of the IVA algorithm as it is used to model the nonlinear dependency structure within the source vectors. An alternative multivariate Student's t distribution source prior is proposed for the IVA algorithm as it is known to be well suited for modelling certain speech signals due to its heavy tail nature. Therefore the nonlinear score function that is derived from the proposed Student's t source prior can better model the dependency structure within the frequency bins and thereby enhance the separation performance and the convergence speed of the IVA and the Fast version of the IVA (FastIVA) algorithms. 4 5 A novel energy driven mixed Student's t and the original super Gaussian source prior is also proposed for the IVA algorithms. As speech signals can be composed of many high and low amplitude data points, therefore the Student's t distribution in the mixed source prior can account for the high amplitude data points whereas the original su- per Gaussian distribution can cater for the other information in the speech signals. Furthermore, the weight of both distributions in the mixed source prior can be ad- justed according to the energy of the observed mixtures. Therefore the mixed source prior adapts the measured signals and further enhances the performance of the IVA algorithm. A common approach within the IVA algorithm is to model di erent speech sources with an identical source prior, however this does not account for the unique characteristics of each speech signal. Therefore dependency modelling for di erent speech sources can be improved by modelling di erent speech sources with di erent source priors. Hence, the Student's t mixture model (SMM) is introduced as a source prior for the IVA algorithm. This new source prior can adapt according to the nature of di erent speech signals and the parameters for the proposed SMM source prior are estimated by deriving an e cient expectation maximization (EM) algorithm. As a result of this study, a novel EM framework for the IVA algorithm with the SMM as a source prior is proposed which is capable of separating the sources in an e cient manner. The proposed algorithms are tested in various realistic reverberant room environments with real speech signals. All the experiments and evaluation demonstrate the robustness and enhanced separation performance of the proposed algorithms

New Negentropy Optimization Schemes for Blind Signal Extraction of Complex Valued Sources

Blind signal extraction, a hot issue in the field of communication signal processing, aims to retrieve the sources through the optimization of contrast functions. Many contrasts based on higher-order statistics such as kurtosis, usually behave sensitive to outliers. Thus, to achieve robust results, nonlinear functions are utilized as contrasts to approximate the negentropy criterion, which is also a classical metric for non-Gaussianity. However, existing methods generally have a high computational cost, hence leading us to address the problem of efficient optimization of contrast function. More precisely, we design a novel “reference-based” contrast function based on negentropy approximations, and then propose a new family of algorithms (Alg.1 and Alg.2) to maximize it. Simulations confirm the convergence of our method to a separating solution, which is also analyzed in theory. We also validate the theoretic complexity analysis that Alg.2 has a much lower computational cost than Alg.1 and existing optimization methods based on negentropy criterion. Finally, experiments for the separation of single sideband signals illustrate that our method has good prospects in real-world applications

A stochastic algorithm for probabilistic independent component analysis

The decomposition of a sample of images on a relevant subspace is a recurrent problem in many different fields from Computer Vision to medical image analysis. We propose in this paper a new learning principle and implementation of the generative decomposition model generally known as noisy ICA (for independent component analysis) based on the SAEM algorithm, which is a versatile stochastic approximation of the standard EM algorithm. We demonstrate the applicability of the method on a large range of decomposition models and illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multi-Detector Multi-Component spectral matching and applications for CMB data analysis

We present a new method for analyzing multi--detector maps containing contributions from several components. Our method, based on matching the data to a model in the spectral domain, permits to estimate jointly the spatial power spectra of the components and of the noise, as well as the mixing coefficients. It is of particular relevance for the analysis of millimeter--wave maps containing a contribution from CMB anisotropies.Comment: 15 pages, 7 Postscript figures, submitted to MNRA

Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps

We propose to model the image differentials of astrophysical source maps by Student's t-distribution and to use them in the Bayesian source separation method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC) sampling scheme to unmix the astrophysical sources and describe the derivation details. In this scheme, we use the Langevin stochastic equation for transitions, which enables parallel drawing of random samples from the posterior, and reduces the computation time significantly (by two orders of magnitude). In addition, Student's t-distribution parameters are updated throughout the iterations. The results on astrophysical source separation are assessed with two performance criteria defined in the pixel and the frequency domains.Comment: 12 pages, 6 figure

Bayesian source separation with mixture of Gaussians prior for sources and Gaussian prior for mixture coefficients

In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians [Moulines97] and the mixing matrix elements distributions by a Gaussian [Djafari99a]. We model the mixture of Gaussians hierarchically by mean of hidden variables representing the labels of the mixture. Then, we consider the joint a posteriori distribution of sources, mixing matrix elements, labels of the mixture and other parameters of the mixture with appropriate prior probability laws to eliminate degeneracy of the likelihood function of variance parameters and we propose two iterative algorithms to estimate jointly sources, mixing matrix and hyperparameters: Joint MAP (Maximum a posteriori) algorithm and penalized EM algorithm. The illustrative example is taken in [Macchi99] to compare with other algorithms proposed in literature. Keywords: Source separation, Gaussian mixture, classification, JMAP algorithm, Penalized EM algorithm.Comment: Presented at MaxEnt00. Appeared in Bayesian Inference and Maximum Entropy Methods, Ali Mohammad-Djafari(Ed.), AIP Proceedings (http://proceedings.aip.org/proceedings/confproceed/568.jsp