High-Order Contrasts for Self-Adaptive Source Separation

Moreau, Éric; Macchi, Odile

doi:10.1002/(sici)1099-1115(199601)10:1<19::aid-acs384>3.0.co;2-7

Cited by 116 publications

(52 citation statements)

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“…(55)) the asymptotic performance index in eqs. (54) and (55) depend only on some statistical moments the stability of the adaptive algorithms (42) also depends only on the values of i 's even better, the trajectory (43) of the global system C t = B t A does not depend on A whose sole e ect is to determine the initial point.…”

Section: Equivariance and Uniform Performancementioning

confidence: 99%

Blind signal separation: statistical principles

1998

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Abstract| Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or`sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem, to show how they stem from basic principles and how they relate to each other.

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Section: Equivariance and Uniform Performancementioning

confidence: 99%

Blind signal separation: statistical principles

1998

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“…The indexes based on cumulants have a long history and several authors have proposed them in many different ways and forms [3], [15], [27], [37]. The higher order cumulants of the outputs can be used in data corrupted by additive Gaussian noise because they are asymptotically invariant to the presence of such noise in the mixture.…”

Section: Cumulants Based Indexesmentioning

confidence: 99%

“…When one knows a priori, the probability density function of the desired sources , , it seems reasonable to consider a factorial model for the joint-probability density function of the observations as in (37) where is the known joint pdf of the subset of desired sources, while is a complementary pdf which condenses all the remaining ignorance about the model. Assuming a stationary i.i.d.…”

Section: A Maximum Likelihoodmentioning

confidence: 99%

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From Blind Signal Extraction to Blind Instantaneous Signal Separation: Criteria, Algorithms, and Stability

Cruces

Cichocki

Амари

2004

IEEE Trans. Neural Netw.

101

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Abstract-This paper reports a study on the problem of the blind simultaneous extraction of specific groups of independent components from a linear mixture. This paper first presents a general overview and unification of several information theoretic criteria for the extraction of a single independent component. Then, our contribution fills the theoretical gap that exists between extraction and separation by presenting tools that extend these criteria to allow the simultaneous blind extraction of subsets with an arbitrary number of independent components. In addition, we analyze a family of learning algorithms based on Stiefel manifolds and the natural gradient ascent, present the nonlinear optimal activations (score) functions, and provide new or extended local stability conditions. Finally, we illustrate the performance and features of the proposed approach by computer-simulation experiments.Index Terms-Blind-signal extraction, blind signal separation, independent component analysis, negentropy and minimum entropy, projection pursuit.

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“…Equivalences with the Godard [5] (or constant modulus [6]) criterion have since been placed in evidence [7], [8], as have relations with mutual information criteria and contrast functions [9]- [11]. This has motivated numerous contributions in a wide range of multisource signal separation and/or deconvolution settings [12]- [17].…”

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confidence: 99%

Properties of some blind equalization criteria in noisy multiuser environments

Regalia¹,

Mboup

2001

IEEE Trans. Signal Process.

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Abstract-Blind equalization in noisy multiuser channels has met with increasing attention with the advent of multiaccess digital communication systems. We examine blind equalizer performance in cases where perfect equalization proves unattainable due to noise and interference from concurrent users. In particular, we obtain a characterization of stationary points and extrema for a family of blind criteria in "undermodeled" cases, which assimilates the influence of differing source statistics and background noise correlation properties; relations to mean-square equalization measures are then obtained as a byprocuct. By re-examining a gradient search procedure, we obtain domains of attraction of each extremum in a special "sufficient order" setting. We also derive a global step-size bound for undermodeled cases, which ensures convergence of a gradient search procedure to an extremum of a blind cost function. We likewise confirm that the super-exponential algorithm results from an optimal choice of this step-size parameter.Index Terms-Blind equalization, minimum entropy methods, undermodeled equalizatiopn, multiaccess communications, superexponential algorithm.

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High-Order Contrasts for Self-Adaptive Source Separation

Cited by 116 publications

References 1 publication

Blind signal separation: statistical principles

Blind signal separation: statistical principles

From Blind Signal Extraction to Blind Instantaneous Signal Separation: Criteria, Algorithms, and Stability

Properties of some blind equalization criteria in noisy multiuser environments

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