Convolutive mixtures of signals, which are common in acoustic environments, can be difficult to separate into their component sources. Here we present a uniform probabilistic framework to separate convolutive mixtures of acoustic signals using independent vector analysis (IVA), which is based on a joint distribution for the frequency components originating from the same source and is capable of preventing permutation disorder. Different gaussian mixture models (GMM) served as source priors, in contrast to the original IVA model, where all sources were modeled by identical multivariate Laplacian distributions. This flexible source prior enabled the IVA model to separate different type of signals. Three classes of models were derived and tested: noiseless IVA, online IVA, and noisy IVA. In the IVA model without sensor noise, the unmixing matrices were efficiently estimated by the expectation maximization (EM) algorithm. An online EM algorithm was derived for the online IVA algorithm to track the movement of the sources and separate them under nonstationary conditions. The noisy IVA model included the sensor noise and combined denoising with separation. An EM algorithm was developed that found the model parameters and separated the sources simultaneously. These algorithms were applied to separate mixtures of speech and music. Performance as measured by the signal-to-interference ratio (SIR) was substantial for all three models.

While the sample-spacings-based density estimation method is simple and efficient, its applicability has been restricted to one-dimensional data. In this letter, the method is generalized such that it can be extended to multiple dimensions in certain circumstances. As a consequence, a multidimensional entropy estimator of spherically invariant continuous random variables is derived. Partial bias of the estimator is analyzed, and the estimator is further used to derive a nonparametric objective function for frequency-domain independent component analysis. The robustness and the effectiveness of the objective function are demonstrated with simulation results.

This paper presents a novel adaptive approach to the separation of convolutedly mixed acoustic signals based on independent vector analysis (IVA). IVA, as an extension of independent component analysis (ICA) from univariate components to multivariate components, provides an efficient framework for avoiding the well-known permutation problem in frequency-domain blind source separation (BSS). However, since IVA has been mostly employing pre-specified and simple source priors which are good fits to speech signals, the performance degrades when the mixture includes unknown sources other than speech. Also, sensor noise has not been considered. To tackle these limitations, we employ multivariate Gaussian mixture model (GMM) as the source priors and add sensor noise into the model. We derive an expectation maximization (EM) algorithm that estimates the separating matrices and the parameters of the unknown source prior together. The performance is demonstrated by experimental results that include the comparison with the IVA results using fixed source priors.

We propose a new blind source separation approach that models the inherent signal dependencies such as those observed in speech signals in order to solve the problem of separating convolved sources. The frequency domain methods for the convolved mixture problem require a solution to the well-known permutation problem. Our approach is based on assuming a vector representation of the source signal where its multidimensional joint densities are non-spherical. Spherical distributions may be adequate for signals that exhibit uniform dependencies across frequencies but in case of speech signals we can observe stronger dependencies for neighboring frequency bins and almost no dependency for frequency bins that are far apart. The non-spherical joint density model takes into account this phenomenon. For the separation of convolved sources, the proposed method demonstrates consistent performance over previous methods and improved performance over the spherical joint density representations.

A new consistent objective function for nonparametric complex independent component analysis (ICA) is proposed where the complex variables are restricted to be circular, or radially symmetric. This objective function is derived using an order statistics based density estimator which orders the complex data by their absolute values. The objective function is unconditional to the source distribution other than the circularity and it measures the statistical independence directly from the data. Using this objective function, a nonparametric complex independent component analysis algorithm can be derived. Also, the generalization of this objective function allows it to be combined with other algorithms to increase their separation performances. Experiments demonstrate the usefulness of the new objective function.

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in frequency-domain blind source separation. Instead of running ICA in each frequency bin and matching the permutation afterwards, IVA exploits the dependency among the frequency components of a source and deal with them altogether as a multivariate data by capturing the dependency with a multivariate joint probability density function (PDF). For modelling the frequency components of speech, sparse and spherically symmetric PDFs have been chosen. In this paper, we compare the separation performance of IVA with a group of PDFs where the density is uniformly distributed for the data points of the same lp-norm value by changing both the value of p and the sparseness. Also we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimension. Simulation results show that sparseness and spherical symmetry together is a good assumption for the speech model in the frequency domain.

A new independent component analysis (ICA) formulation called independent vector analysis (IVA) was proposed in order to solve the permutation problem in convolutive blind source separation (BSS). Instead of running ICA in each frequency bin separately and correcting the disorder with an additional algorithmic scheme afterwards, IVA exploited the dependency among the frequency components of a source and dealt with them as a multivariate source by modeling it with sparse and spherically, or radially, symmetric joint probability density functions (pdfs). In this paper, we compare the speech separation performances of IVA by using a group of lp-norm-invariant sparse pdfs where the value of and the sparseness can be controlled. Also, we derive an IVA algorithm from a nonparametric perspective with the constraint of spherical symmetry and high dimensionality. Simulation results confirm the efficiency of assuming sparseness and spherical symmetry for the speech model in the frequency domain.