Robert Aichner

A generalization of blind source separation algorithms for convolutive mixtures based on second-order statistics

We present a general broadband approach to blind source separation (BSS) for convolutive mixtures based on second-order statistics. This avoids several known limitations of the conventional narrowband approximation, such as the internal permutation problem. In contrast to traditional narrowband approaches, the new framework simultaneously exploits the nonwhiteness property and nonstationarity property of the source signals. Using a novel matrix formulation, we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms by generalizing a known cost-function which inherently allows joint optimization for several time-lags of the correlations. Based on the broadband approach time-domain, constraints are obtained which provide a deeper understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both the time-domain and the frequency-domain versions, we discuss links to well-known, and also, to novel algorithms that constitute special cases. Moreover, using the so-called generalized coherence, links between the time-domain and the frequency-domain algorithms can be established, showing that our cost function leads to an update equation with an inherent normalization ensuring a robust adaptation behavior. The concept is applicable to offline, online, and block-online algorithms by introducing a general weighting function allowing for tracking of time-varying real acoustic environments.

Blind Source Separation for Convolutive Mixtures: A Unified Treatment

Blind source separation (BSS) algorithms for time series can exploit three properties of the source signals: nonwhiteness, nonstationarity, and nongaussianity. While methods utilizing the first two properties are usually based on second-order statistics (SOS), higher-order statistics (HOS) must be considered to exploit nongaussianity. In this chapter, we consider all three properties simultaneously to design BSS algorithms for convolutive mixtures within a new generic framework. This concept derives its generality from an appropriate matrix notation combined with the use of multivariate probability densities for considering the time-dependencies of the source signals. Based on a generalized cost function we rigorously derive the corresponding time-domain and frequency-domain broadband algorithms. Due to the broadband approach, time-domain constraints are obtained which provide a more detailed understanding of the internal permutation problem in traditional narrowband frequency-domain BSS. For both, the time-domain and the frequency-domain versions, we discuss links to well-known and also to novel algorithms that follow as special cases of the framework. Moreover, we use models for correlated spherically invariant random processes (SIRPs) which are well suited for a variety of source signals including speech to obtain efficient solutions in the HOS case. The concept provides a basis for off-line, online, and block-on-line algorithms by introducing a general weighting function, thereby allowing for tracking of time-varying real acoustic environments.

A real-time blind source separation scheme and its application to reverberant and noisy acoustic environments

In this paper, we present an efficient real-time implementation of a broadband algorithm for blind source separation (BSS) of convolutive mixtures. A recently introduced generic BSS framework based on a matrix formulation allows simultaneous exploitation of nonwhiteness and nonstationarity of the source signals using second-order statistics. We demonstrate here that this general scheme leads to highly efficient real-time algorithms based on block-online adaptation suitable for ordinary PC platforms. Moreover, we investigate the problem of incorporating noncausal delays which are necessary with certain geometric constellations. Furthermore, the robustness against diffuse background noise, eg., in a car environment is examined and a stepsize control is proposed which further enhances the robustness in real-world environments and leads to an improvement in separation performance. The algorithms were investigated in a reverberant office room and in noisy car environments verifying that the proposed method ensures high separation performance in realistic scenarios.

TRINICON-based Blind System Identification with Application to Multiple-Source Localization and Separation

This contribution treats blind system identification approaches and how they can be used to localize multiple sources in environments where multipath propagation cannot be neglected, e.g., acoustic sources in reverberant environments. Based on TRINICON, a general framework for broadband adaptive MIMO signal processing, we first derive a versatile blind MIMO system identification method. For this purpose, the basics of TRINICON will be reviewed to the extent needed for this application, and some new algorithmic aspects will be emphasized. The generic approach then allows us to study various illustrative relations to other algorithms and applications. In particular, it is shown that the optimization criteria used for blind system identification allow a generalization of the well-known Adaptive Eigen- value Decomposition (AED) algorithm for source localization: Instead of one source as with AED, several sources can be localized simultaneously. Performance evalu- ation in realistic scenarios will show that this method compares favourably with other state-of-the-art methods for source localization.

Post-Processing for Convolutive Blind Source Separation

Convolutive blind source separation (BSS) aims at separating point sources from mixtures picked up by several sensors. In real-world environments moving speakers, background noise and long reverberation are encountered which often degrade the performance of BSS algorithms. In such cases, the application of a post-filter can improve the output signal quality by suppression of residual cross-talk and of background noise. In this paper we propose a novel technique to estimate the necessary power spectral densities of the cross-talk components and present a robust system which allows to further suppress both, the remaining interference from point sources and the background noise. Experimental results show the benefit of this post-processing method in realistic environments

Real-Time Convolutive Blind Source Separation Based on a Broadband Approach

In this paper we present an efficient real-time implementation of a broadband algorithm for blind source separation (BSS) of convolutive mixtures. A recently introduced matrix formulation allows straightforward simultaneous exploitation of nonwhiteness and nonstationarity of the source signals using second-order statistics. We examine the efficient implementation of the resulting algorithm and introduce a block-on-line update method for the demixing filters. Experimental results for moving speakers in a reverberant room show that the proposed method ensures high separation performance. Our method is implemented on a standard laptop computer and works in realtime.

Exploiting narrowband efficiency for broadband convolutive blind source separation

Based on a recently presented generic broadband blind source separation (BSS) algorithm for convolutive mixtures, we propose in this paper a novel algorithm combining advantages of broadband algorithms with the computational efficiency of narrowband techniques. By selective application of the Szegö theorem which relates properties of Toeplitz and circulant matrices, a new normalization is derived as a special case of the generic broadband algorithm. This results in a computationally efficient and fast converging algorithm without introducing typical narrowband problems such as the internal permutation problem or circularity effects. Moreover, a novel regularization method for the generic broadband algorithm is proposed and subsequently also derived for the proposed algorithm. Experimental results in realistic acoustic environments show improved performance of the novel algorithm compared to previous approximations.

A novel normalization and regularization scheme for broadband convolutive blind source separation

In this paper we propose a novel blind source separation (BSS) algorithm for convolutive mixtures combining advantages of broadband algorithms with the computational efficiency of narrowband techniques. It is based on a recently presented generic broadband algorithm. By selective application of the Szego theorem which relates properties of Toeplitz and circulant matrices, a new normalization is derived which approximates well the exact normalization of the generic broadband algorithm presented in [2]. The new scheme thus results in a computationally efficient and fast converging algorithm while still avoiding typical narrowband problems such as the internal permutation problem or circularity effects. Moreover, a novel regularization method for the generic broadband algorithm is proposed and subsequently also derived for the proposed algorithm. Experimental results in realistic acoustic environments show improved performance of the novel algorithm compared to previous approximations.