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The algorithm for nonnegative blind source separation using edge feature

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Abstract

The Nonnegative Blind Source Separation (NBSS) algorithm based on Minimum Volume Simplex (MVS) has a high dependence on the convex hull of mixed scatterplot, in addition, the shape of convex hull is variable, which increases the uncertainty of the algorithm, therefore, algorithms based on MVS have some restrictions on the shape of mixed scatterplot. Particularly, in the most extreme case, i.e. when the mixing system is ill conditioned and the scatterplot degenerates from n-dimension to (n−1)-dimension, these algorithms almost lose the ability of unmixing. On the other hand, the shape of the mixed scatterplot of sparse signals such as speech is generally fixed, specifically, it is an inclined cross in the two-dimension case. This paper proposes an algorithm based on the slope distribution of edge feature scatters. After sparsity mixtures by extracting edge features, the edge feature scatterplot with inclined cross shape can be obtained. By statistical the slope distribution of edge feature scatterplot, the optimal estimation of the mixing matrix can be found by finding the interval extremum of the slope distribution. In order to improve the accuracy of the geometric method, this paper proposes a Minimum Jaccard Index (MJI) criterion to judge whether the estimation of the mixed matrix is optimal or not. The proposed method does not need the assumption of source independence, or even the locally dominant assumption or pure pixel assumption often mentioned in algorithms based on MVS, and this method only needs the source boundedness assumption indeed. Our method is robust to ill condition, which enriches the theory and method of bounded component analysis and makes up for the shortcomings of other related algorithms.

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Acknowledgements

This work is supported by National Key Research and Development Program(Grant No. 2017YFB1002804): Multimodal Data Interaction Intention Understanding in Cloud Fusion and Major Project of National Social Science Foundation of China (Grant No.17ZDA331): Methodology Research on Thinking of Chinese Medicine (2017-2022).

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Authors and Affiliations

  1. School of Computer & Communication Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Mingzhan Zhao, Zhiliang Wang & Zhimin Zhang

  2. Information Engineering College of HeBei University of Architecture, HeBei University Of Architecture, Zhangjiakou, 075000, China

    Mingzhan Zhao, Zhen Zhao & Zhen Dong

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  1. Mingzhan Zhao
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Zhao, M., Wang, Z., Zhao, Z. et al. The algorithm for nonnegative blind source separation using edge feature. SIViP 16, 897–904 (2022). https://doi.org/10.1007/s11760-021-02032-y

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