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Journal of Applied Mathematics and Computation

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

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

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

Date: September 15,2022 Hits: 404

Abstract

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.

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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