Blind separation of instantaneous mixtures of nonstationary sources

By Dinh Tuan Pham, Jean-François Cardoso. IEEE Transactions on Signal Processing, 2001

561 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Signal Processing

View Paper: https://www.semanticscholar.org/paper/12cd5a80fbac96f11212d71ce53f9915b57f351c

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In Analytical Chemistry

In Signal Processing

Citations in the corpus

Bubbles: a unifying framework for low-level statistical properties of natural image sequences. (2003, background): “nique of blind source separation by nonstationary variance(47) assumes a smoothly changing variance signal.(48) This formulation can be shown to be related to energy correlation.”
Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA (2016, background): “Our definition thus generalizes the linear model [22, 24, 16] to the nonlinear case, as well as to very general modulated non-Gaussian densities by allowing qi,v to be non-quadratic, using more than one qi,v per source (i.”
Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity (2010, methodology): “In such a case, it might also be advantageous to change the LiNGAM estimation method so that the ICA part is replaced by methods estimating (4) explicitly based on temporal heteroscedasticity (Matsuoka et al., 1995; Hyvärinen, 2001; Pham and Cardoso, 2001); this is quite straightforward and necessit”
Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning (2018, background): “These generalize earlier identifiability conditions for linear ICA [2, 20].”
THE THREE EASY ROUTES TO INDEPENDENT COMPONENT ANALYSIS; CONTRASTS AND GEOMETRY (2001, background): “Marginal non properties The above definitions of ‘non properties’ also apply to each component E 4 (each row) ofE , that is, to variables.”
Advances in Nonlinear Blind Source Separation (2003, background): “If the source signals are not plain random variables but have a temporal structure, linear blind source separation can be achieved by utilizing either temporal correlations [19], [20] or nonstationarity [21], [22] under somewhat different assumptions; see [1], Chapter 18.”
Charrelation Matrix Based ICA (2012, background): “…addresses weighted approximate joint diagonalization (AJD) of matrixform statistics (frequently termed target matrices) having the appealing property of being strictly diagonal for random vectors with independent components, such as in JADE [1], SOBI [2], BGL [3] and (more recently) WITCHESS [4].”
Independent component analysis: recent advances (2013, methodology): “Under suitable assumptions, joint (approximate) diagonalization of such covariance matrices estimates the ICA model, and a number of algorithms have been developed for such joint diagonalization (Belouchrani et al., 1997; Pham and Cardoso, 2001; Yeredor, 2010).”
Adaptive blind signal and image processing (2002, background): “There are some recent works on nonstationary source separation [223, 224, 968] (see Chapters 4, 6 and 8 for overview and).”
Blind Source Separation and Independent Component Analysis : A Review (2004, methodology): “Second-order non-stationarity was also exploited in [122], but only noise-free data was considered.”
A Link between the Canonical Decomposition in Multilinear Algebra and Simultaneous Matrix Diagonalization (2006, methodology): “Simultaneous matrix decompositions have become an important tool for signal processing and data analysis in the last decade [2, 3, 8, 19, 23, 35 , 36, 42, 43, 44].”
A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources (2005, background): “However, the approaches presented in [7–9] do not apply to the underdetermined case, as they then yield signals which are still mixtures of all source signals.”
Watermarking security: theory and practice (2005, background): “The following theoretical derivations (as well as the algorithm used in experiments in section V) can be adapted to colored original signals and even non stationary original signals [24].”
Geometric source separation: merging convolutive source separation with geometric beamforming (2001, methodology): “A similar diagonalization criterion, based on the maximum likelihood (ML) cost assuming multivariate Gaussian distributions, was presented in [28], .”
Causal Discovery with General Non-Linear Relationships using Non-Linear ICA (2019, methodology): “As expected, the Joint Diagonal-ization algorithm of Pham and Cardoso (2001) suffers a drop in performance.”
Time-Domain Blind Separation of Audio Sources on the Basis of a Complete ICA Decomposition of an Observation Space (2011, methodology): “The ICA is a stochastic method whose accuracy measured in terms of the interferenceto-signal ratio is, in theory, proportional to the number of components M ; see for example [24], [28], [29].”