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A geometric blind source separation method based on facet component analysis

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Abstract

Given a set of mixtures, blind source separation attempts to retrieve the source signals without or with very little information of the mixing process. We present a geometric approach for blind separation of nonnegative linear mixtures termed facet component analysis. The approach is based on facet identification of the underlying cone structure of the data. Earlier works focus on recovering the cone by locating its vertices (vertex component analysis) based on a mutual sparsity condition which requires each source signal to possess a stand-alone peak in its spectrum. We formulate alternative conditions so that enough data points fall on the facets of a cone instead of accumulating around the vertices. To find a regime of unique solvability, we make use of both geometric and density properties of the data points and develop an efficient facet identification method by combining data classification and linear regression. For noisy data, total variation technique may be employed. We show computational results on nuclear magnetic resonance spectroscopic data to substantiate our method.

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Acknowledgments

The work was partially supported by NSF-ATD grants DMS-0911277 and DMS-122507.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Penghang Yin & Jack Xin

  2. Department of Mathematics and Statistics, Florida International University, Miami, FL, 33199, USA

    Yuanchang Sun

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  1. Penghang Yin
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  2. Yuanchang Sun
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Correspondence to Yuanchang Sun.

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Yin, P., Sun, Y. & Xin, J. A geometric blind source separation method based on facet component analysis. SIViP 10, 19–28 (2016). https://doi.org/10.1007/s11760-014-0696-6

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  • DOI: https://doi.org/10.1007/s11760-014-0696-6

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