Advances in Blind Source Separation (Bss) and Independent Component Analysis (Ica) for Nonlinear Mixtures

Jutten, Christian; Karhunen, Juha

doi:10.1142/s012906570400208x

Cited by 124 publications

(92 citation statements)

References 65 publications

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“…Existing nonlinear BSS methods have been reviewed in [16,17], and earlier in Chapter 17 of the book [1]. The paper [16] reviews especially uniqueness results on nonlinear ICA and BSS, separation methods for post-nonlinear mixtures, and our variational Bayesian estimation methods, referring to papers in which the detailed results have been presented.…”

Section: Existing Methodsmentioning

confidence: 99%

“…Blind separation of sources from their nonlinear mixtures-known as nonlinear blind source separation (BSS)-is generally a difficult problem, both from a theoretical and a practical point of view [1,16,17]. The task is to extract the sources s(t) that have generated the observations x(t) through a nonlinear mapping f (·):…”

Section: Nonlinear Blind Source Separationmentioning

confidence: 99%

“…But the extension to the nonlinear mixture model (1) is difficult since both the nonlinear mapping and the underlying sources must be learned from the data in a blind manner, and the problem is highly ill-posed without suitable regularisation [18,1,16]. The independence assumption used in ICA is no longer sufficient for achieving separation.…”

Section: Nonlinear Blind Source Separationmentioning

confidence: 99%

“…, M, are first mixed linearly according to the basic linear ICA/BSS model (2), but after that nonlinear functions f i are applied to them to get the final observations x i . It can be shown [19,16] that for the noiseless post-nonlinear mixtures, the indeterminacies are usually the same as for the basic linear instantaneous ICA model (2). That is, the sources can be separated or the independent components estimated up to the scaling, permutation, and sign indeterminacies assuming the post-nonlinearities f i are invertible and under weak conditions on the mixing matrix A and source distributions.…”

Section: Nonlinear Blind Source Separationmentioning

confidence: 99%

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Blind separation of nonlinear mixtures by variational Bayesian learning

Honkela¹,

Valpola²,

Ilin³

et al. 2007

Digital Signal Processing

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Blind separation of sources from nonlinear mixtures is a challenging and often illposed problem. We present three methods for solving this problem: an improved nonlinear factor analysis (NFA) method using multilayer perceptron (MLP) network to model the nonlinearity, a hierarchical NFA (HNFA) method suitable for larger problems and a post-nonlinear NFA (PNFA) method for more restricted post-nonlinear mixtures. The methods are based on variational Bayesian learning, which provides the needed regularisation and allows for easy handling of missing data. While the basic methods are incapable of recovering the correct rotation of the source space, they can discover the underlying nonlinear manifold and allow reconstruction of the original sources using standard linear independent component analysis (ICA) techniques.

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Section: Existing Methodsmentioning

confidence: 99%

Section: Nonlinear Blind Source Separationmentioning

confidence: 99%

Section: Nonlinear Blind Source Separationmentioning

confidence: 99%

Section: Nonlinear Blind Source Separationmentioning

confidence: 99%

See 2 more Smart Citations

Blind separation of nonlinear mixtures by variational Bayesian learning

Honkela¹,

Valpola²,

Ilin³

et al. 2007

Digital Signal Processing

Self Cite

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“…We introduced different measures of nongaussianity [21] i.e. objective functions for ICA estimation.…”

Section: The Fastica Algorithmmentioning

confidence: 99%

Blind Image Separation based on a Flexible Parametric Distribution Function

Otaibi¹

2017

IJCA

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The blind image separation has been widely investigated nowadays. As a result, many algorithms of feature extraction have been developed for direct application of such image structures. One example of this, the separation of mixed fingerprints found in a crime scene, in which a mixture of two or more fingerprints may be gathered, for identification, they must be separated. In this paper, we propose a new technique for multiple mixed images separation based on modified Weibull distribution. We use an efficient method based on genetic algorithm and maximum likelihood for estimating the parameters of such score functions. Also the accuracy of this proposed distribution is measured, and we compare the algorithmic performance using the efficient approach with some other previous distributions. The numerical results show that the proposed distribution is flexible and has efficient results.

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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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Advances in Blind Source Separation (Bss) and Independent Component Analysis (Ica) for Nonlinear Mixtures

Cited by 124 publications

References 65 publications

Blind separation of nonlinear mixtures by variational Bayesian learning

Blind separation of nonlinear mixtures by variational Bayesian learning

Blind Image Separation based on a Flexible Parametric Distribution Function

Blind Source Separation and Blind Mixture Identification Methods

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