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Multi-Source Localization and Signal Extraction Using a Proximal Gradient-based Compressed Sensing Approach

Date: September 15,2022 |Hits: 341 Download PDF How to cite this paper

Chun-Shian Tao1, Yu-An Chen1, Yi-Cheng Hsu1,*, Mingsian R. Bai1,2

1Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan, China.

2Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan, China.

*Corresponding author: Yi-Cheng Hsu


This paper presents a computationally efficient algorithm for multiple source localization and signal extraction (SLSE). Posed as an underdetermined system, a novel compressed sensing (CS) algorithm is proposed to address SLSE problems in one stage. A Least Absolute and Selection Operator (LASSO) problem is first formulated and solved jointly for the source locations and signal amplitudes. A computationally efficient and noise-resilient algorithm is developed on the basis of the complex Proximal Gradient (Proxgrad) method. It follows that the nonzero entries of the optimal solutions give rise to the amplitudes and directions of sound sources. To further enhance the separation quality, soft thresholds based on W-disjoint orthogonality is exploited. Experiments are conducted to compare the proposed SLSE method with several baselines in terms of localization and separation metrics. The results showed that the proposed LASSO-Proxgrad algorithm yielded superior localization and signal extraction performance with the minimal processing time compared to the baselines.


[1] Rascon, C., & Meza, I. (2017). Localization of sound sources in robotics: A review. Robotics and Autonomous Systems, 96, 184-210. https://doi.org/10.1016/j.robot.2017.07.011.

[2] Bian, X., Abowd, G. D., & Rehg, J. M. (2005, May). Using sound source localization in a home environment. In International Conference on Pervasive Computing, Springer, Berlin, Heidelberg, 19-36. https://doi.org/10.1007/11428572_2.

[3] Marti, A., Cobos, M., & Lopez, J. J. (2011, May). Real time speaker localization and detection system for camera steering in multiparticipant videoconferencing environments. In 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2592-2595.

[4] Brown, G. J., & Wang, D. (2005). Separation of speech by computational auditory scene analysis. In Speech enhancement, Springer, Berlin, Heidelberg, 371-402.

[5] Kotus, J., Lopatka, K., & Czyzewski, A. (2014). Detection and localization of selected acoustic events in acoustic field for smart surveillance applications. Multimedia Tools and Applications, 68(1), 5-21. https://doi.org/10.1007/s11042-012-1183-0.

[6] Yang, M., & De Hoog, F. (2015). Orthogonal matching pursuit with thresholding and its application in compressive sensing. IEEE Transactions on Signal Processing, 63(20), 5479-5486. https://doi.org/10.1109/TSP.2015.2453137.

[7] Li, J., Wu, Z., Feng, H., Wang, Q., & Liu, Y. (2014, May). Greedy orthogonal matching pursuit algorithm for sparse signal re-covery in compressive sensing. In 2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, 1355-1358.

[8] Dorfan, Y., Schwartz, O., Schwartz, B., Habets, E. A., & Gannot, S. (2016, November). Multiple DOA estimation and blind source separation using estimation-maximization. In 2016 IEEE International Conference on the Science of Electrical Engineering (ICSEE), 1-5.

[9] Çöteli, M. B., & Hacıhabiboğlu, H. (2021). Sparse Representations With Legendre Kernels for DOA Estimation and Acoustic Source Separation. IEEE/ACM Transactions on Audio, Speech, and Language Processing, 29, 2296-2309. https://doi.org/10.1109/TASLP.2021.3091845.

[10] Bai, M. R., Lan, S. S., Huang, J. Y., Hsu, Y. C., & So, H. C. (2020). Audio enhancement and intelligent classification of house-hold sound events using a sparsely deployed array. The Journal of the Acoustical Society of America, 147(1), 11-24. https://doi.org/10.1121/10.0000492.

[11] Bai, M. R., & Chen, C. C. (2013). Application of convex optimization to acoustical array signal processing. Journal of Sound and Vibration, 332(25), 6596-6616. https://doi.org/10.1016/j.jsv.2013.07.029.

[12] Gerstoft, P., Xenaki, A., & Mecklenbräuker, C. F. (2015). Multiple and single snapshot compressive beamforming. The Journal of the Acoustical Society of America, 138(4), 2003-2014. https://doi.org/10.1121/1.4929941.

[13] Chi, Y., Scharf, L. L., Pezeshki, A., & Calderbank, A. R. (2011). Sensitivity to basis mismatch in compressed sensing. IEEE Transactions on Signal Processing, 59(5), 2182-2195. https://doi.org/10.1109/TSP.2011.2112650.

[14] Elad, M. (2010). Sparse and redundant representations: from theory to applications in signal and image processing. New York: springer.

[15] Cai, T. T., & Wang, L. (2011). Orthogonal matching pursuit for sparse signal recovery with noise. IEEE Transactions on Infor-mation theory, 57(7), 4680-4688. https://doi.org/10.1109/TIT.2011.2146090.

[16] Lilis, G. N., Angelosante, D., & Giannakis, G. B. (2010). Sound field reproduction using the lasso. IEEE Transactions on Audio, Speech, and Language Processing, 18(8), 1902-1912. https://doi.org/10.1109/TASL.2010.2040523.

[17] Parikh, N., & Boyd, S. (2014). Proximal algorithms. Foundations and trends® in Optimization, 1(3), 127-239.

[18] L. Vandenberghe, “Proximal gradient method,” Ch.4, Lecture notes of ECE236C - Optimization Methods for Large-Scale Systems (Spring 2019), UCLA. http://www.seas.ucla.edu/~vandenbe/ee236c.html.

[19] Rickard, S., & Yilmaz, O. (2002, May). On the approximate W-disjoint orthogonality of speech. In 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASS), I-529-I-532.

[20] Candes, E. J. (2008). The restricted isometry property and its implications for compressed sensing. C. R. l’Academie des Sciences, Ser. I, no. 346, 589-592.

[21] Chen, A. I., & Ozdaglar, A. (2012, October). A fast distributed proximal-gradient method. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing, 601-608.

[22] Habets, E. A., Cohen, I., & Gannot, S. (2008). Generating nonstationary multisensor signals under a spatial coherence constraint. The Journal of the Acoustical Society of America, 124(5), 2911-2917. https://doi.org/10.1121/1.2987429.

[23] Guimaraes, D. A., Floriano, G. H. F., & Chaves, L. S. (2015). A tutorial on the CVX system for modeling and solving convex optimization problems. IEEE Latin America Transactions, 13(5), 1228-1257. https://doi.org/10.1109/TLA.2015.7111976.

[24] Hansen, P. C. (1992). Analysis of discrete ill-posed problems by means of the L-curve. SIAM review, 34(4), 561-580. https://doi.org/10.1137/1034115.

How to cite this paper

Multi-Source Localization and Signal Extraction Using a Proximal Gradient-based Compressed Sensing Approach

How to cite this paper:  Chun-Shian Tao, Yu-An Chen, Yi-Cheng Hsu, Mingsian R. Bai. (2022) Multi-Source Localization and Signal Extraction Using a Proximal Gradient-based Compressed Sensing Approach. Journal of Applied Mathematics and Computation6(3), 347-355.

DOI: http://dx.doi.org/10.26855/jamc.2022.09.007

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