Blind separation of convolutive mixtures using second and fourth order moments

In this paper we present a simple efficient local unsupervised learning algorithm for on-line adaptive multichannel blind deconvolution and separation of i.i.d. sources. Under mild conditions, there exits a stable inverse system so that the source signals can be exactly recovered from their convolutive mixtures. Based on the existence of the inverse filter, we construct a two-stage neural network which consists of blind equalization and source separation. In blind equalization stage, we employ anti-Hebbian learning in temporal domain for decorrelation. For blind separation, we can apply any existing algorithms. Extensive computer simulations confirm the validity and high performance of our proposed learning algorithm.

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“…Note that this result is consistent with some results in [12,13]. Suppose that H(z) is full rank for all z.…”

Section: Sketch Of Proofsupporting

confidence: 90%

“…This is emphasized in [12,13] where whitening is done by linear prediction. In contrast to [12,13], our approach is more robust in the sense that we do not need exact knowledge of the order of channels.…”

Section: Sketch Of Proofmentioning

confidence: 99%

Blind signal deconvolution by spatio-temporal decorrelation and demixing

Choi

Cichocki²

Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop

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“…A typical assumption in this area is that the number of sources is less than the number of observations. Icart and Gautier (1996) present a method in which the generative model of Eq. (5) is modelled using an auto-regressive moving average (ARMA) model.…”

Section: B Anechoic Mixingmentioning

confidence: 99%

Survey of sparse and non‐sparse methods in source separation

O’Grady

Pearlmutter

Rickard

2005

Int J Imaging Syst Tech

145

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Source separation arises in a variety of signal processing applications, ranging from speech processing to medical image analysis. The separation of a superposition of multiple signals is accomplished by taking into account the structure of the mixing process and by making assumptions about the sources. When the information about the mixing process and sources is limited, the problem is called ''blind'. By assuming that the sources can be represented sparsely in a given basis, recent research has demonstrated that solutions to previously problematic blind source separation problems can be obtained. In some cases, solutions are possible to problems intractable by previous non-sparse methods. Indeed, sparse methods provide a powerful approach to the separation of linear mixtures of independent data. This paper surveys the recent arrival of sparse blind source separation methods and the previously existing nonsparse methods, providing insights and appropriate hooks into theliterature along the way.

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“…Numerous methods have been used in the published literature to indicate separation performance. The list includes mean-square-error (MSE) [20], [21] bit per symbol error rate [22], [23], Frobenius distance [24], multichannel row and multichannel column intersymbol interference (ISI) [25], plot of global mixing filter responses [26]- [28], signal-to-noise ratio (SNR) [29]- [31], interference-to-signal ratio (ISR) [19], signal-to-interference ratio (SIR) [32]- [38], one-at-a-time SIR [8], ISI [39]- [41], bias and standard deviation of filter coefficients [42], [43], plot of estimated sources in the time or frequency domain [44]- [46], hand-segmented SIR [47], automatic speech recognition rate [48], [33], [34], and the mean opinion score [18]. Several of these are not ideal for comparisons because they are either subjective, such as the plots and the mean opinion score, or require knowledge of the mixing filters, which makes them inapplicable for real mixtures.…”

Section: Figures Of Merit For Separationmentioning

confidence: 99%

Experimental upper bound for the performance of convolutive source separation methods

Hild

Erdoğmuş

Prı́ncipe

2006

IEEE Trans. Signal Process.

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Abstract-An important problem in the field of blind source separation (BSS) of real convolutive mixtures is the determination of the role of the demixing filter structure and the criterion/optimization method in limiting separation performance. This issue requires the knowledge of the optimal performance for a given structure, which is unknown for real mixtures. Herein, the authors introduce an experimental upper bound on the separation performance for a class of convolutive blind source separation structures, which can be used to approximate the optimal performance. As opposed to a theoretical upper bound, the experimental upper bound produces an estimate of the optimal separating parameters for each dataset in addition to specifying an upper bound on separation performance. Estimation of the upper bound involves the application of a supervised learning method to the set of observations found by recording the sources one at a time. Using the upper bound, it is demonstrated that structures other than the finite-impulse-response (FIR) structure should be considered for real (convolutive) mixtures, there is still much room for improvement in current convolutive BSS algorithms, and the separation performance of these algorithms is not necessarily limited by local minima.Index Terms-Blind source separation (BSS), convolutive source separation, independent components analysis (ICA), speech enhancement, upper bound.

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Blind separation of convolutive mixtures using second and fourth order moments

Cited by 13 publications

References 4 publications

Blind signal deconvolution by spatio-temporal decorrelation and demixing

Blind signal deconvolution by spatio-temporal decorrelation and demixing

Survey of sparse and non‐sparse methods in source separation

Experimental upper bound for the performance of convolutive source separation methods

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