Underdetermined blind source separation has received increasing attention in recent years as an effective method for speech-signal processing. Hence, a self-organizing mapping-density peak clustering and compressed sensing approach, which is a two-step approach, is proposed herein to improve the accuracy of underdetermined blind source separation. The approach features the following two aspects: (1) A mixing matrix estimation method based on self-organizing mapping and density peak clustering, which can intuitively determine the number of source signals, remove outliers, and determine the column vector of the mixing matrix based on local density; (2) a compressed sensing-based source signal reconstruction method, which can exploit the sparsity of signals in the frequency domain and use a hierarchical coupling method to reconstruct the source signal accurately and efficiently under the premise that the prior knowledge of the signal is unknown. The proposed method does not require the number of source signals and exhibits excellent performance under different noise conditions. Theoretical analysis and experimental results demonstrate the effectiveness of the proposed method.

1. [1] A. Sadhu, S. Narasimhan, and J. Antoni, “A review of output-only structural mode identification literature employing blind source separation methods,” Mechanical Systems and Signal Processing, Vol.94, pp. 415-431, 2017. https://doi.org/10.1016/j.ymssp.2017.03.001
2. [2] A. E. A. Ferreira and D. Alarcão, “Real-time blind source separation system with applications to distant speech recognition,” Applied Acoustics, Vol.113, pp. 170-184, 2016. https://doi.org/10.1016/j.apacoust.2016.06.024
3. [3] R. R. Vázquez, H. Vélez-Pérez, R. Ranta et al., “Blind source separation, wavelet denoising and discriminant analysis for EEG artefacts and noise cancelling,” Biomedical Signal Processing and Control, Vol.7, No.4, pp. 389-400, 2012. https://doi.org/10.1016/j.bspc.2011.06.005
4. [4] L. Zou, X. Chen, G. Dang et al., “Removing Muscle Artifacts from EEG Data via Underdetermined Joint Blind Source Separation: A Simulation Study,” IEEE Trans. on Circuits and Systems II: Express Briefs, Vol.67, No.1, pp. 187-191, 2020. https://doi.org/10.1109/TCSII.2019.2903648
5. [5] G. Li, G. Tang, H. Wang, and Y. Wang, “Blind source separation of composite bearing vibration signals with low-rank and sparse decomposition,” Measurement, Vol.145, pp. 323-334, 2019. https://doi.org/10.1016/j.measurement.2019.05.099
6. [6] Q. Wang, Y. Zhang, S. Yin et al., “A Novel Underdetermined Blind Source Separation Method Based on OPTICS and Subspace Projection,” Symmetry, Vol.13, No.9, Article No.1677, 2021. https://doi.org/10.3390/sym13091677
7. [7] K. Yu, K. Yang, and Y. Bai, “Estimation of modal parameters using the sparse component analysis based underdetermined blind source separation,” Mechanical Systems and Signal Processing, Vol.45, No.2, pp. 302-316, 2014. https://doi.org/10.1016/j.ymssp.2013.11.018
8. [8] L. Zhen, D. Peng, H. Zhang et al., “Underdetermined Mixing Matrix Estimation by Exploiting Sparsity of Sources,” Measurement, Vol.152, Article No.107268, 2020. https://doi.org/10.1016/j.measurement.2019.107268
9. [9] L. Zou, X. Chen, and Z. Wang, “Underdetermined Joint Blind Source Separation for Two Datasets Based on Tensor Decomposition,” IEEE Signal Processing Letters, Vol.23, No.5, pp. 673-677, 2016. https://doi.org/10.1109/LSP.2016.2546687
10. [10] Y. Li, A. Cichocki, and S. Amari, “Analysis of Sparse Representation and Blind Source Separation,” Neural Computation, Vol.16, No.6, pp. 1193-1234, 2004. https://doi.org/10.1162/089976604773717586
11. [11] N. Fu and X. Peng, “K-Hough Underdetermined Blind Mixing Model Recovery Algorithm,” J. of Electronic Measurement and Instrument, Vol.22, No.5, pp. 63-67, 2008.
12. [12] F. Amini and Y. Hedayati, “Underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis,” J. of Sound and Vibration, Vol.366, pp. 117-132, 2016. https://doi.org/10.1016/j.jsv.2015.10.028
13. [13] X.-S. He, F. He, and W.-H. Cai, “Underdetermined BSS Based on K-means and AP Clustering,” Circuits, Syst., Signal Process., Vol.35, pp. 2881-2913, 2016. https://doi.org/10.1007/s00034-015-0173-7
14. [14] J. Sun, Y. Li, J. Wen, and S. Yan, “Novel mixing matrix estimation approach in underdetermined blind source separation,” Neurocomputing, Vol.173, Part 3, pp. 623-632, 2016. https://doi.org/10.1016/j.neucom.2015.08.008
15. [15] A. Asaei, H. Bourlard, M. J. Taghizadeh et al., “Computational methods for underdetermined convolutive speech localization and separation via model-based sparse component analysis,” Speech Communication, Vol.76, pp. 201-217, 2016. https://doi.org/10.1016/j.specom.2015.07.002
16. [16] G. Ruan, Q. Guo, and J. Gao, “Novel underdetermined blind source separation algorithm based on compressed sensing and K-SVD,” Trans. on Emerging Telecommunications Technologies, Vol.29, No.9, Article No.e3427, 2018. https://doi.org/10.1002/ett.3427
17. [17] L. Sun, K. Xie, T. Gu et al., “Joint Dictionary Learning Using a New Optimization Method for Single-Channel Blind Source Separation,” Speech Communication, Vol.106, pp. 85-94, 2018. https://doi.org/10.1016/j.specom.2018.11.008
18. [18] T. Kohonen, “Self-organized formation of topologically correct feature maps,” Biological Cybernetics, Vol.43, pp. 59-69, 1982. https://doi.org/10.1007/BF00337288
19. [19] A. Rodriguez and A. Laio, “Clustering by fast search and find of density peaks,” Science, Vol.344, No.6191, pp. 1492-1496, 2014. https://doi.org/10.1126/science.1242072
20. [20] P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Processing, Vol.81, No.11, pp. 2353-2362, 2001. https://doi.org/10.1016/S0165-1684(01)00120-7
21. [21] T.-Y. Sun, C.-C. Liu, S.-J. Tsai et al., “Cluster Guide Particle Swarm Optimization (CGPSO) for Underdetermined Blind Source Separation with Advanced Conditions,” IEEE Trans. on Evolutionary Computation, Vol.15, No.6, pp. 798-811, 2011. https://doi.org/10.1109/TEVC.2010.2049361
22. [22] L. Zhen, D. Peng, Z. Yi et al., “Underdetermined Blind Source Separation Using Sparse Coding,” IEEE Trans. on Neural Networks and Learning Systems, Vol.28, No.12, pp. 3102-3108, 2017. https://doi.org/10.1109/TNNLS.2016.2610960
23. [23] Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition,” Proc. of 27th Asilomar Conf. on Signals, Systems and Computers, Vol.1, pp. 40-44, 1993. https://doi.org/10.1109/ACSSC.1993.342465
24. [24] M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Trans. on Signal Processing, Vol.54, No.11, pp. 4311-4322, 2006. https://doi.org/10.1109/TSP.2006.881199