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A survey on one-bit compressed sensing: theory and applications

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Abstract

In the past few decades, with the growing popularity of compressed sensing (CS) in the signal processing field, the quantization step in CS has received significant attention. Current research generally considers multi-bit quantization. For systems employing quantization with a sufficient number of bits, a sparse signal can be reliably recovered using various CS reconstruction algorithms.

Recently, many researchers have begun studying the one-bit quantization case for CS. As an extreme case of CS, one-bit CS preserves only the sign information of measurements, which reduces storage costs and hardware complexity. By treating one-bit measurements as sign constraints, it has been shown that sparse signals can be recovered using certain reconstruction algorithms with a high probability. Based on the merits of one-bit CS, it has been widely applied to many fields, such as radar, source location, spectrum sensing, and wireless sensing network.

In this paper, the characteristics of one-bit CS and related works are reviewed. First, the framework of one-bit CS is introduced. Next, we summarize existing reconstruction algorithms. Additionally, some extensions and practical applications of one-bit CS are categorized and discussed. Finally, our conclusions and the further research topics are summarized.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61302084).

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Authors and Affiliations

  1. Key Lab of Universal Wireless Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Zhilin Li, Wenbo Xu, Xiaobo Zhang & Jiaru Lin

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  1. Zhilin Li
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  2. Wenbo Xu
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Correspondence to Zhilin Li.

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Zhilin Li received the BE degree in communication engineering from the Minzu University of China, China in 2011. He is currently pursuing the PhD degree in the School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, China. His current research interests include signal processing in wireless communication, compressed sensing, and machine learning.

Wenbo Xu received the BS and PhD degrees from School of Information Engineering in Beijing University of Posts and Telecommunications (BUPT), China in 2005 and 2010, respectively. She is currently an associate professor in the School of Information and Communication Engineering in BUPT. Her research interests include signal processing in wireless networks and digital signal processing.

Xiaobo Zhang received the MS degree from School of Mathematics and Statistics, Zheng Zhou University, China in 2014. He is currently working toward the PhD degree at the School of Information Engineering, Beijing University of Posts and Telecommunications, China. His research interests include compressive sensing, combination design, measure and probability.

Jiaru Lin received the BS and PhD degrees from School of Information Engineering in Beijing University of Posts and Telecommunications (BUPT), China in 1987 and 2001, respectively. From 1991 to 1994, he studied in Swiss Federal Institute of Technology Zurich, Switzerland. He is now a professor and PhD supervisor in the School of Information and Communication Engineering, BUPT. His research interests include wireless communication, personal communication and communication networks.

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Li, Z., Xu, W., Zhang, X. et al. A survey on one-bit compressed sensing: theory and applications. Front. Comput. Sci. 12, 217–230 (2018). https://doi.org/10.1007/s11704-017-6132-7

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