Blind separation of sources that have spatiotemporal variance dependencies

In blind source separation methods, the sources are typically assumed to be independent. Some methods are also able to separate dependent sources by estimating or assuming a parametric model for their dependencies. Here, we propose a method that separates dependent sources without a parametric model of their dependency structure. This is possible by introducing some general assumptions on the structure of the dependencies: the sources are dependent only through their variances (general activity levels), and the variances of the sources have temporal correlations. The method can be called double-blind because of this additional blind aspect: We do not need to estimate (or assume) a parametric model of the dependencies, which is in stark contrast to most previous methods.

[1]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[2]  Pierre Comon.  Independent component analysis - a new concept? signal processing , 1994 .

[3]  Aapo Hyvärinen,et al.  Topographic Independent Component Analysis , 2001, Neural Computation.

[4]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[5]  SorouchyariF..  Blind separation of sources, Part III , 1991 .

[6]  Schuster,et al.  Separation of a mixture of independent signals using time delayed correlations. , 1994, Physical review letters.

[7]  Nathalie Delfosse,et al.  Adaptive blind separation of independent sources: A deflation approach , 1995, Signal Process..

[8]  Michael I. Jordan,et al.  Tree-dependent Component Analysis , 2002, UAI.

[9]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  Kiyotoshi Matsuoka,et al.  A neural net for blind separation of nonstationary signals , 1995, Neural Networks.

[12]  Eero P. Simoncelli,et al.  Random Cascades on Wavelet Trees and Their Use in Analyzing and Modeling Natural Images , 2001 .

[13]  Erkki Oja,et al.  Independent Component Analysis for Identification of Artifacts in Magnetoencephalographic Recordings , 1997, NIPS.

[14]  Aapo Hyvärinen,et al.  Blind source separation by nonstationarity of variance: a cumulant-based approach , 2001, IEEE Trans. Neural Networks.

[15]  Aapo Hyvärinen,et al.  Simple-Cell-Like Receptive Fields Maximize Temporal Coherence in Natural Video , 2003, Neural Computation.

[16]  Jean-François Cardoso,et al.  Multidimensional independent component analysis , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[17]  Dinh-Tuan Pham,et al.  Blind Partial Separation of Instantaneous Mixtures of Sources , 2006, ICA.

[18]  Aapo Hyvärinen,et al.  Bubbles: a unifying framework for low-level statistical properties of natural image sequences. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[19]  Aapo Hyvärinen,et al.  Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces , 2000, Neural Computation.

[20]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[21]  A. Hyvärinen,et al.  Temporal and spatiotemporal coherence in simple-cell responses: a generative model of natural image sequences , 2003, Network.

[22]  Juha Karhunen,et al.  Hierarchical models of variance sources , 2004, Signal Process..

[23]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[24]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixtures of nonstationary sources , 2001, IEEE Trans. Signal Process..

[25]  Lang Tong,et al.  Indeterminacy and identifiability of blind identification , 1991 .