A blind source separation technique using second-order statistics

By Adel Belouchrani, Karim Abed-Meraim, Jean-François Cardoso, Eric Moulines. 1997

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “Many do this to uncover and disentangle hidden underlying sources of signals (e.g., Jutten and Herault, 1991; Schuster, 1992; Andrade et al., 1993; Molgedey and Schuster, 1994; Comon, 1994; Cardoso, 1994; Bell and Sejnowski, 1995; Karhunen and Joutsensalo, 1995; Belouchrani et al., 1997; Hyvärinen e”
Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Series (2020, methodology): “For linear ICA this approach has been shown to yield identiﬁable models (Belouchrani et al., 1997; Tong et al., 1991), and extensions to the nonlinear case have been also been proposed in earlier work (Harmel-ing et al., 2003; Sprekeler et al., 2014).”
The Sound of Pixels (2018, background): “While auditory scene analysis [1] is widely studied in the fields of environmental sound recognition [2,3] and source separation [4,5,6,7,8,9], the natural synchronization between vision and sound can provide a rich supervisory signal for grounding sounds in vision [10,11,12].”
Adaptive blind signal and image processing (2002, background): “In fact the SONS is a generalization of the SOBI [86, 90] to the case of nonstationary sources.”
Blind Source Separation and Independent Component Analysis : A Review (2004, methodology): “It provides identical or at least very similar decomposition of raw data as the well known and popular SOBI and TDSEP algorithms [19] [153].”
Recipes for the linear analysis of EEG (2005, methodology): “Most ICA algorithms are based on simultaneous diagonalization of multiple (more than two) cross-moments such as JADE (Cardoso and Souloumiac, 1993, 1996), SOBI (Belouchrani et al., 1997), or multiple decorrelations (Parra and Spence, 2000; Parra and Sajda, 2003; Pham and Cardoso, 2001; Ziehe et al.,”
Independent component analysis: recent advances (2013, methodology): “…to estimate the ICA model even for Gaussian data, based on the time structure (autocorrelations) alone, as initially pointed out by Tong et al. (1991) and further developed by Belouchrani et al. (1997) among others (see Chapter 18 of (Hyvärinen et al., 2001) or (Yeredor, 2010) for reviews.)”
Blind source separation based vibration mode identification (2007, methodology): “To this end various methods have been developed, such as AMUSE [15], SOBI [16], temporal decorrelation separation (TDSEP) [24] or time– frequency blind source separation (TFBSS) [25].”
Handbook of Blind Source Separation: Independent Component Analysis and Applications (2010, methodology): “…of vector a traceA trace of matrix A detA determinant of matrix A meana arithmetic average of component of vector a š(ν) Fourier transform of process s(t) ⊗ Kronecker product between matrices ⊗ tensor product •j contraction over index j krank{A} Kruskal’s k-rank of matrix A Contents Glossary 3”
Blind detection of independent dynamic components (2001, background): “Independent component analysis (ICA) is typically based on non-Gaussianity [3, 4] or temporal correlations [5, 6].”
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis (2014, background): “Among many such examples, the Nth-order moments (cumulants) of a vector-valued random variable form an Nth-order tensor [9], while in second-order ICA snapshots of data statistics (covariance matrices) are effectively slices of a third-order tensor [12], [37].”
Probabilistic updating of building models using incomplete modal data (2016, methodology): “Herein, a secondorder blind identification (SOBI) [55] approach is used to identify the modal responses and mode shapes.”
Tensor Decomposition for Signal Processing and Machine Learning (2016, background): “This approach to source separation was pioneered by Belouchrani [90].”
Canonical Correlation Analysis Applied to Remove Muscle Artifacts From the Electroencephalogram (2006, methodology): “The comparison with temporal decorrelation-based ICA techniques (TDSEP [15], ac-dc [16], SOBI [11], etc.) and the mathematical relationship between CCA and these techniques will be the subject of further research.”
Blind separation of nonstationary sources in noisy mixtures (2000, methodology): “The mixing matrix is estimated by pre-whitening the data followed by a unitary transformation which jointly diagonalize cumulant matrices [2] or time-delayed correlation matrices [5, 4, 1].”