Blind separation of non stationary sources using joint block diagonalization

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

doi:10.1109/ssp.2001.955319

Cited by 13 publications

(18 citation statements)

References 6 publications

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“…These criteria are different than our KLD-based criterion, which will be presented shortly. A KLD criterion for JBD, in the context of source separation, has first been suggested by [3], in order to separate one-dimensional sources from their convolutive mixture; however, [3] do not specify the algorithm used to minimize their criterion. The fast algorithm for joint diagonalization via KLD minimization, suggested by Pham [4], is extended for JBD of cyclostationary sources in [5].…”

Section: Introductionmentioning

confidence: 99%

Joint Block Diagonalization Algorithms for Optimal Separation of Multidimensional Components

Lahat

Jean-Fran$#

Cardoso

et al. 2012

Latent Variable Analysis and Signal Separation

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Abstract. This paper deals with non-orthogonal joint block diagonalization. Two algorithms which minimize the Kullback-Leibler divergence between a set of real positive-definite matrices and a block-diagonal transformation thereof are suggested. One algorithm is based on the relative gradient, and the other is based on a quasi-Newton method. These algorithms allow for the optimal, in the mean square error sense, blind separation of multidimensional Gaussian components. Simulations demonstrate the convergence properties of the suggested algorithms, as well as the dependence of the criterion on some of the model parameters.

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Section: Introductionmentioning

confidence: 99%

Joint Block Diagonalization Algorithms for Optimal Separation of Multidimensional Components

Lahat

Jean-Fran$#

Cardoso

et al. 2012

Latent Variable Analysis and Signal Separation

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“…and Q is the number of distinct equations in (26). The factorization in (26) is often referred to as JBD (e.g., [25]). In analogy to (10), each summand in (25)…”

Section: A a Link Between Jisa And Isamentioning

confidence: 99%

“…Theorem VIII. 3: Consider an ISA model whose sufficient statistics are given by (25), where A ∈ R M ×M is a nonsingular matrix, and {S (q ) ii } Q q =1 a sequence of positive-definite realvalued symmetric m i × m i matrices, irreducible by simultaneous congruence (Definition VIII.2), for any i = 1, . .…”

Section: A a Link Between Jisa And Isamentioning

confidence: 99%

“…The fact that certain results on the uniqueness of tensor decompositions are special cases of results on the uniqueness of a more general class of coupled block decompositions (8) hints that other fundamental concepts in the analysis of the uniqueness of tensor decompositions, such as Kruskal's rank [53], generalize as well. We point out that the concept of Kruskal's rank was generalized in [46] for matrices partitioned column-wise into blocks, however, not for block elements such as {S (25), which are m i × m i × Q tensors and not matrices. We leave further discussion of this topic to future publications.…”

Section: B Implications On Block-based Decompositionsmentioning

confidence: 99%

“…A similar FIM-based approach was used in [19], in the identifiability analysis of ISA of piecewise-stationary overdetermined Gaussian multivariate processes. Similarly to JISA and CBD, this ISA model can be represented algebraically, through joint block diagonalization (JBD) of its correlation matrices [25]. Therefore, ISA identifiability can be recast in algebraic terms of JBD uniqueness.…”

Section: Introductionmentioning

confidence: 99%

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Joint Independent Subspace Analysis: Uniqueness and Identifiability

Lahat¹,

Jutten

2019

IEEE Trans. Signal Process.

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This paper deals with the identifiability of joint independent subspace analysis (JISA). JISA is a recently-proposed framework that subsumes independent vector analysis (IVA) and independent subspace analysis (ISA). Each underlying mixture can be regarded as a dataset; therefore, JISA can be used for data fusion. In this paper, we assume that each dataset is an overdetermined mixture of several multivariate Gaussian processes, each of which has independent and identically distributed samples. This setup is not identifiable when each mixture is considered individually. Given these assumptions, JISA can be restated as coupled block diagonalization (CBD) of its correlation matrices. Hence, JISA identifiability is tantamount to CBD uniqueness. In this work, we provide necessary and sufficient conditions for uniqueness and identifiability of JISA and CBD. Our analysis is based on characterizing all the cases in which the Fisher information matrix is singular. We prove that non-identifiability may occur only due to pairs of underlying random processes with the same dimension. Our results provide further evidence that irreducibility has a central role in the uniqueness analysis of block-based decompositions. Our contribution extends previous results on the uniqueness and identifiability of ISA, IVA, coupled matrix and tensor decompositions. We provide examples to illustrate our results. Index Terms-Blind source separation, block decompositions, coupled decompositions, data fusion, identifiability, independent vector analysis, uniqueness.Dana Lahat received the Ph.D. degree in electrical engineering from Tel Aviv University, Tel Aviv, Israel, in 2013. She is currently a Postdoctoral Researcher with the Toulouse

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