Herbert Buchner

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.

TRINICON: a versatile framework for multichannel blind signal processing

In this paper we present a framework for multichannel blind signal processing for convolutive mixtures, such as blind source separation (BSS) and multichannel blind deconvolution (MCBD). It is based on the use of multivariate pdf and a compact matrix notation which considerably simplifies the representation and handling of the algorithms. By introducing these techniques into an information theoretic cost function, we can exploit the three fundamental signal properties nonwhiteness, nongaussianity, and nonstationarity. This results in a versatile tool that we call TRINICON (Triple-N ICA for convolutive mixtures). Both, links to popular algorithms and several novel algorithms follow from the general approach. In particular, we introduce a new concept of multichannel blind partial deconvolution (MCBPD) for speech which prevents a complete whitening of the output signals, i.e., the vocal tract is excluded from the equalization. This is especially interesting for automatic speech recognition applications. Moreover, we show results for BSS using multivariate spherically invariant random processes (SIRP) to efficiently model speech, and show how the approach carries over to MCBPD. These concepts are also suitable for an efficient implementation in the frequency domain by using a rigorous broadband derivation avoiding the internal permutation problem and circularity effects.

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.

Active listening room compensation for massive multichannel sound reproduction systems using wave-domain adaptive filtering

The acoustic theory for multichannel sound reproduction systems usually assumes free-field conditions for the listening environment. However, their performance in real-world listening environments may be impaired by reflections at the walls. This impairment can be reduced by suitable compensation measures. For systems with many channels, active compensation is an option, since the compensating waves can be created by the reproduction loudspeakers. Due to the time-varying nature of room acoustics, the compensation signals have to be determined by an adaptive system. The problems associated with the successful operation of multichannel adaptive systems are addressed in this contribution. First, a method for decoupling the adaptation problem is introduced. It is based on a generalized singular value decomposition and is called eigenspace adaptive filtering. Unfortunately, it cannot be implemented in its pure form, since the continuous adaptation of the generalized singular value decomposition matrices to the variable room acoustics is numerically very demanding. However, a combination of this mathematical technique with the physical description of wave propagation yields a realizable multichannel adaptation method with good decoupling properties. It is called wave domain adaptive filtering and is discussed here in the context of wave field synthesis.

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.

Acoustic Echo Cancellation for Surround Sound using Perceptually Motivated Convergence Enhancement

Acoustic echo cancellation (AEC) has become an essential and well-known enabling technology for hands-free communication and human-machine interfaces. AEC for two or more reproduction channels aims at identifying the echo paths between the microphone and each audio reproduction source in order to cancel the associated echo contribution. A number of preprocessing methods have been proposed to decorrelate stereo audio signals in order to enable an unambiguous identification of each echo path and to thus ensure robustness to changing sound source locations. While several of these methods provide enough decorrelation to achieve proper AEC convergence in the stereo case, considerations of subjective sound quality have frequently not been addressed adequately. This paper compares the performance of several methods in terms of both convergence speed and aspects of sound perception, and proposes a novel signal decorrelation approach with attractive properties. The superior performance of the proposed method is demonstrated for 5.1 surround sound reproduction.

Generalized multichannel frequency-domain adaptive filtering: efficient realization and application to hands-free speech communication

In unknown environments where we need to identify, model, or track unknown and time-varying channels, adaptive filtering has been proven to be an effective tool. In this contribution, we focus on multichannel algorithms in the frequency domain that are especially well suited for input signals which are not only auto-correlated but also highly cross-correlated among the channels. These properties are particularly important for applications like multichannel acoustic echo cancellation. Most frequency-domain algorithms, as they are well known from the single-channel case, are derived from existing time-domain algorithms and are based on different heuristic strategies, e.g, for stepsize normalization. Here, we present a new rigorous derivation of a whole class of multichannel adaptive filtering algorithms in the frequency domain based on a recursive least-squares criterion. Then, from the normal equation, we derive a generic adaptive algorithm in the frequency domain. Due to the rigorous approach, the proposed framework inherently takes the coherence between all input signal channels into account. An analysis of this multichannel algorithm shows that the mean-squared error convergence is independent of the input signal statistics (i.e., both auto-correlation and cross-correlation). A useful approximation provides interesting links between some well-known algorithms for the single-channel case and the general multichannel framework. We also give design rules for important parameters to optimize the performance in practice. The computational complexity is kept low by introducing several new techniques, such as a robust recursive Kalman gain computation in the frequency domain and efficient fast Fourier transform (FFT) computation tailored to overlapping data blocks. Simulation results and real-time performance for applications such as multichannel acoustic echo cancellation show the high efficiency of the approach.

Simultaneous localization of multiple sound sources using blind adaptive MIMO filtering

Blind adaptive filtering for time delay of arrival (TDOA) estimation is a very powerful method for acoustic source localization in reverberant environments with broadband signals like speech. Based on a recently presented generic framework for blind signal processing for convolutive mixtures, called TRINICON, we present a TDOA estimation method for simultaneous multidimensional localization of multiple sources. Moreover, an interesting link to the known single-input multiple-output (SIMO)-based adaptive eigenvalue decomposition (AED) method is shown. We evaluate the novel multiple-input multiple-output (MIMO)-based approach and compare it with the known SIMO-based method in a reverberant acoustic environment using reference data of the positions obtained from infrared sensors. The results show that the new approach is very robust against reverberation and background noise.

Robust extended multidelay filter and double-talk detector for acoustic echo cancellation

We propose an integrated acoustic echo cancellation solution based on a novel class of efficient and robust adaptive algorithms in the frequency domain, the extended multidelay filter (EMDF). The approach is tailored to very long adaptive filters and highly auto-correlated input signals as they arise in wideband full-duplex audio applications. The EMDF algorithm allows an attractive tradeoff between the well-known multidelay filter and the recursive least-squares algorithm. It exhibits fast convergence, superior tracking capabilities of the signal statistics, and very low delay. The low computational complexity of the conventional frequency-domain adaptive algorithms can be maintained thanks to efficient fast realizations. We also show how this approach can be combined efficiently with a suitable double-talk detector (DTD). We consider a corresponding extension of a recently proposed DTD based on a normalized cross-correlation vector whose performance was shown to be superior compared to other DTDs based on the cross-correlation coefficient. Since the resulting DTD also has an EMDF structure it is easy to implement, and the fast realization also carries over to the DTD scheme. Moreover, as the robustness issue during double talk is particularly crucial for fast-converging algorithms, we apply the concept of robust statistics into our extended frequency-domain approach. Due to the robust generalization of the cost function leading to a so-called M-estimator, the algorithms become inherently less sensitive to outliers, i.e., short bursts that may be caused by inevitable detection failures of a DTD. The proposed structure is also well suited for an efficient generalization to the multichannel case

TDOA Estimation for Multiple Sound Sources in Noisy and Reverberant Environments Using Broadband Independent Component Analysis

In this paper, we show that minimization of the statistical dependence using broadband independent component analysis (ICA) can be successfully exploited for acoustic source localization. As the ICA signal model inherently accounts for the presence of several sources and multiple sound propagation paths, the ICA criterion offers a theoretically more rigorous framework than conventional techniques based on an idealized single-path and single-source signal model. This leads to algorithms which outperform other localization methods, especially in the presence of multiple simultaneously active sound sources and under adverse conditions, notably in reverberant environments. Three methods are investigated to extract the time difference of arrival (TDOA) information contained in the filters of a two-channel broadband ICA scheme. While for the first, the blind system identification (BSI) approach, the number of sources should be restricted to the number of sensors, the other methods, the averaged directivity pattern (ADP) and composite mapped filter (CMF) approaches can be used even when the number of sources exceeds the number of sensors. To allow fast tracking of moving sources, the ICA algorithm operates in block-wise batch mode, with a proportionate weighting of the natural gradient to speed up the convergence of the algorithm. The TDOA estimation accuracy of the proposed schemes is assessed in highly noisy and reverberant environments for two, three, and four stationary noise sources with speech-weighted spectral envelopes as well as for moving real speech sources.