Jacobi-like algorithm for blind signal separationof convolutivemixtures

Bousbia-Salah, H.; Belouchrani, Adel; Abed-Meraim, Karim

doi:10.1049/el:20010698

Cited by 33 publications

(25 citation statements)

References 4 publications

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“…X is usually interpreted as an instantaneous mixture, X = AS, where S is a matrix constructed of delayed original signals analogously to X, and A is a mixing matrix that has the block-Sylvester structure. However, such mixture is equivalent with (1) in full if only A has more columns than rows, m > d and L is sufficiently large; see [9], [10].…”

Section: Bmentioning

confidence: 99%

“…Most often a matrix is defined so that its rows contain the time-lagged copies of signals from microphones, and the observation space is spanned by these rows. In general, TD methods aim at finding subspaces of the observation space that correspond to separated signals [9].…”

Section: Introductionmentioning

confidence: 99%

“…The complete decomposition is usually constrained by an assumption that the inverse of the decomposing transform (matrix) has a special structure, for example block-Toeplitz or block-Sylvester; see articles of Kellermann et al and Belouchrani et al, e.g. [9], [14], [15]. Févotte et al proposed a two-stage separation procedure in [10] doing the complete decomposition by an algorithm for the independent subspace analysis (ISA) through joint block diagonalization (JBD) [9] utilizing the orthogonal constraint [17].…”

Section: Introductionmentioning

confidence: 99%

“…[9], [14], [15]. Févotte et al proposed a two-stage separation procedure in [10] doing the complete decomposition by an algorithm for the independent subspace analysis (ISA) through joint block diagonalization (JBD) [9] utilizing the orthogonal constraint [17]. The algorithm of Douglas et al [18] is an example of a constrained partial decomposition.…”

Section: Introductionmentioning

confidence: 99%

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Time-Domain Blind Separation of Audio Sources on the Basis of a Complete ICA Decomposition of an Observation Space

Koldovsky

Tichavský

2011

IEEE Trans. Audio Speech Lang. Process.

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Abstract-Time-domain algorithms for blind separation of audio sources can be classified as being based either on a partial or complete decomposition of an observation space. The decomposition, especially the complete one, is mostly done under a constraint to reduce the computational burden. However, this constraint potentially restricts the performance. The authors propose a novel time-domain algorithm that is based on a complete unconstrained decomposition of the observation space. The observation space may be defined in a general way, which allows application of long separating filters, although its dimension is low. The decomposition is done by an appropriate independent component analysis (ICA) algorithm giving independent components that are grouped into clusters corresponding to the original sources. Components of the clusters are combined by a reconstruction procedure after estimating microphone responses of the original sources. The authors demonstrate by experiments that the method works effectively with short data, compared to other methods.

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Section: Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time-Domain Blind Separation of Audio Sources on the Basis of a Complete ICA Decomposition of an Observation Space

Koldovsky

Tichavský

2011

IEEE Trans. Audio Speech Lang. Process.

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“…Tensor decompositions with banded matrix factors and possibly also (block-) Toeplitz/Hankel structures have found application in signal processing, in particular in cumulant based blind identification of convolutive mixtures [5,22,2,3,12,13] and in tensor based blind equalization of wireless communication systems [10,20,1]. In this case the banded structure of the matrix factors are directly related to the filter orders of the given system we attempt to identify.…”

Section: Introductionmentioning

confidence: 99%

Tensor decompositions with banded matrix factors

Sørensen¹,

Comon²

2013

Linear Algebra and its Applications

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The computation of the model parameters of a canonical polyadic decomposition (CPD), also known as the parallel factor (PARAFAC) or canonical decomposition (CANDECOMP) or CP decomposition, is typically done by resorting to iterative algorithms, e.g. either iterative alternating least squares type or descent methods. In many practical problems involving tensor decompositions such as signal processing, some of the matrix factors are banded. First, we develop methods for the computation of CPDs with one banded matrix factor. It results in best rank-1 tensor approximation problems. Second, we propose methods to compute CPDs with more than one banded matrix factor. Third, we extend the developed methods to also handle banded and structured matrix factors such as Hankel or Toeplitz. Computer results are also reported.

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Blind Source Separation and Blind Mixture Identification Methods

Deville

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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Blind source separation (BSS) is a generic signal processing problem. BSS methods aim to estimate a set of unknown source signals, by using a set of available signals that are mixtures of the source signals to be restored, with limited or no knowledge of the mixing transform (i.e., the transform of source signals that yields their mixtures). BSS methods were introduced in the 1980s and then quickly expanded. Various books provide a detailed description of BSS methods, or at least of some classes of such methods defined hereafter, such as independent component analysis, sparse component analysis, and nonnegative matrix factorization. Moreover, the BSS problem, focused on signal restoration, is closely linked to the estimation of the mixing transform, and thus to the problem often referred to as blind mixture identification (BMI). In this article, we overview the fields of BSS and BMI. We first define in more detail the considered goal (Section 1) and conditions of investigation (Section 2), and then we introduce the major classes of methods that make it possible to solve the considered problems. The presentation of BSS/BMI methods themselves and of typical applications is given in successive sections (Sections 3–7), where we progress from standard to more advanced configurations, in terms of properties of source signals and class of mixing transform.

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Jacobi-like algorithm for blind signal separationof convolutivemixtures

Cited by 33 publications

References 4 publications

Time-Domain Blind Separation of Audio Sources on the Basis of a Complete ICA Decomposition of an Observation Space

Time-Domain Blind Separation of Audio Sources on the Basis of a Complete ICA Decomposition of an Observation Space

Tensor decompositions with banded matrix factors

Blind Source Separation and Blind Mixture Identification Methods

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