A geometric blind source separation method based on facet component analysis

Penghang Yin Yuanchang Sun Jack Xin

Geometric Modeling and Processing mathscidoc:1912.43886

Signal, Image and Video Processing, 10, (1), 19-28, 2016.1
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 <i>facet component analysis</i>. 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
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@inproceedings{penghang2016a,
  title={A geometric blind source separation method based on facet component analysis},
  author={Penghang Yin, Yuanchang Sun, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210439779371450},
  booktitle={Signal, Image and Video Processing},
  volume={10},
  number={1},
  pages={19-28},
  year={2016},
}
Penghang Yin, Yuanchang Sun, and Jack Xin. A geometric blind source separation method based on facet component analysis. 2016. Vol. 10. In Signal, Image and Video Processing. pp.19-28. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210439779371450.
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