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One-bit compressed sensing reconstruction for block sparse signals

Feng Hui Sun Biao Ma Shu-Gen

One-bit compressed sensing reconstruction for block sparse signals

Feng Hui, Sun Biao, Ma Shu-Gen
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  • Data compression is crucial for resource-constrained signal acquisition and wireless transmission applications with limited data bandwidth. In such applications, wireless data transmission dominates the energy consumption, and the limited telemetry bandwidth could be overwhelmed by the large amount of data generated from multiple sensors. Conventional data compression techniques are computationally intensive, consume large silicon area and offset the energy benefits from reduced data transmission. Recently, compressed sensing (CS) has shown potential in achieving compression performance comparable to previous methods but it has simpler hardware. Especially, one-bit CS theory proves that the signs of compressed measurements contain sufficient information about signal reconstruction, gives that the signals are sparse or compressible in specific dictionaries, thus demonstrating its potential in energy-constrained signal recording and wireless transmission applications. However, the sparsity assumption is too restrictive in many actual scenarios, especially when it is difficult to seek sparse representation for signals. In this paper, a novel one-bit CS method is proposed to reconstruct the signals that are difficult to represent with traditional sparse models. It is capable of recovering signal with comparable compression ratio but avoiding the dictionary selection procedure.The proposed method consists of two parts. 1) The block sparse model is adopted to enforce the structured sparsity of the signals. It not only overcomes the drawbacks of conventional sparse models but also enhances the signal representation accuracy. 2) The probabilistic model of one-bit CS procedure is constructed. Because of the existence of logistic function in probabilistic model of one-bit CS, the Bayesian inference cannot be used to proceed, and the variational Bayesian inference algorithm is developed to reconstruct the original signals from one-bit measurements.Various experiments on different quantities of compressed measurements and iterations are carried out to evaluate the recovery performance of the proposed approach. The photoplethysmography (PPG) signals recorded from subject wrist (dorsal locations) by using PPG sensors built in a wristband are selected as the validation data because they are difficult to represent with traditional sparse dictionaries. The experimental results reveal that the proposed approach outperforms the state-of-the-art one-bit CS method in terms of both reconstruction accuracy and convergence rate.Compared with prior method on one-bit CS, the proposed method shows competitive or superior performance in three aspects. Firstly, by adopting the block sparse model, the proposed method improves the capability to compress signals that are difficult to represent with traditional sparse models, thus making it more practical for long term and real applications. Secondly, by embedding the statistical properties of the one-bit measurements into the recovery algorithm, the proposed method outperforms other one-bit CS methods in terms of both reconstruction performance and convergence speed. Finally, energy and computational efficiency of the proposed method make it an ideal candidate for resource-constrained, large scale, multiple channel signal acquisition and transmission applications.
      Corresponding author: Sun Biao, sunbiao@tju.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61401303, 51578189).
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    Li S D, Chen W F, Yang J, Ma X Y 2016 Acta Phys. Sin. 65 038401(in Chinese)[李少东, 陈文峰, 杨军, 马晓岩2016物理学报 65 038401]

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    Sun B, Zhao W F, Zhu X S 2017 J. Neural Eng. 14 036018

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    Sun B, Feng H, Chen K F, Zhu X S 2016 IEEE Access 4 5169

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    Sun B, Feng H 2017 IEEE Signal Process. Lett. 24 863

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    Sun B, Ni Y M 2017 IEEE Commun. Lett. 21 1775

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    Boufounos P T, Baraniuk R G 2008 Proceedings of the 42nd Annual Conference Information Sciences and Systems Princeton, USA, March 19-21, 2008 p16

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    Sun B, Jiang J J 2011 Acta Phys. Sin. 60 110701(in Chinese)[孙彪, 江建军2011物理学报 60 110701]

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    [15]

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    [16]

    Yang Z, Xie L, Zhang C 2013 IEEE Trans. Signal Process. 61 2815

    [17]

    Meng Q H, Li F 2006 Robot 28 89(in Chinese)[孟庆浩, 李飞2006机器人 28 89]

    [18]

    Cao M L, Meng Q H, Zeng M, Sun B, Li W, Ding C J 2014 Sensors 14 11444

    [19]

    Zhang Z, Jung T P, Makeig S, Rao B 2013 IEEE Trans. Biomed. Eng. 60 221

    [20]

    Zhang Z L 2014 Proceedings of IEEE Global Conference on Signal and Information Processing Atlanta, USA, December 3-5, 2014 p698

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    Zhang Z L, Rao B 2013 IEEE Trans. Signal Process. 61 2009

    [22]

    Tipping M 2001 J. Mach. Learn. Res. 1 211

    [23]

    Tzikas D G, Likas A C, Galatsanos N P 2008 IEEE Signal Process. Mag. 25 131

    [24]

    Bishop C M, Tipping M E 2000 Proceedings of the 16th Conference Uncertainty in Artificial Intelligence San Francisco, USA, June 30-July 3, 2000 p46

    [25]

    Sun B, Feng H, Zhang Z L 2016 Proceedings of the 41st IEEE International Conference on Acoustics, Speech, and Signal Processing Shanghai, China, March 20-25, 2016 p809

    [26]

    Sun B, Zhang Z L 2015 IEEE Sens. J. 15 7161

    [27]

    Li F, Fang J, Li H, Huang L 2015 IEEE Signal Process. Lett. 22 857

  • [1]

    Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289

    [2]

    Candes E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489

    [3]

    Zhang J C, Fu N, Qiao L Y, Peng X Y 2014 Acta Phys. Sin. 63 030701(in Chinese)[张京超, 付宁, 乔立岩, 彭喜元2014物理学报 63 030701]

    [4]

    Li L Z, Yao X R, Liu X F, Yu W K, Zhai G J 2014 Acta Phys. Sin. 63 224201(in Chinese)[李龙珍, 姚旭日, 刘雪峰, 俞文凯, 翟光杰2014物理学报 63 224201]

    [5]

    Li S D, Chen W F, Yang J, Ma X Y 2016 Acta Phys. Sin. 65 038401(in Chinese)[李少东, 陈文峰, 杨军, 马晓岩2016物理学报 65 038401]

    [6]

    Li S D, Chen Y B, Liu R H, Ma X Y 2017 Acta Phys. Sin. 66 038401(in Chinese)[李少东, 陈永彬, 刘润华, 马晓岩2017物理学报 66 038401]

    [7]

    Ning F L, He B J, Wei J 2013 Acta Phys. Sin. 62 174212(in Chinese)[宁方立, 何碧静, 韦娟2013物理学报 62 174212]

    [8]

    Sun B, Zhao W F, Zhu X S 2017 J. Neural Eng. 14 036018

    [9]

    Sun B, Feng H, Chen K F, Zhu X S 2016 IEEE Access 4 5169

    [10]

    Sun B, Feng H 2017 IEEE Signal Process. Lett. 24 863

    [11]

    Sun B, Ni Y M 2017 IEEE Commun. Lett. 21 1775

    [12]

    Boufounos P T, Baraniuk R G 2008 Proceedings of the 42nd Annual Conference Information Sciences and Systems Princeton, USA, March 19-21, 2008 p16

    [13]

    Sun B, Jiang J J 2011 Acta Phys. Sin. 60 110701(in Chinese)[孙彪, 江建军2011物理学报 60 110701]

    [14]

    Boufounos P T 2009 Proceedings of the 43rd Asilomar Conference Signals, Systems and Computers Pacific Grove, USA, November 1-4, 2009 p1305

    [15]

    Jacques L, Laska J N, Boufounos P T, Baraniuk R G 2013 IEEE Trans. Inf. Theory 59 2082

    [16]

    Yang Z, Xie L, Zhang C 2013 IEEE Trans. Signal Process. 61 2815

    [17]

    Meng Q H, Li F 2006 Robot 28 89(in Chinese)[孟庆浩, 李飞2006机器人 28 89]

    [18]

    Cao M L, Meng Q H, Zeng M, Sun B, Li W, Ding C J 2014 Sensors 14 11444

    [19]

    Zhang Z, Jung T P, Makeig S, Rao B 2013 IEEE Trans. Biomed. Eng. 60 221

    [20]

    Zhang Z L 2014 Proceedings of IEEE Global Conference on Signal and Information Processing Atlanta, USA, December 3-5, 2014 p698

    [21]

    Zhang Z L, Rao B 2013 IEEE Trans. Signal Process. 61 2009

    [22]

    Tipping M 2001 J. Mach. Learn. Res. 1 211

    [23]

    Tzikas D G, Likas A C, Galatsanos N P 2008 IEEE Signal Process. Mag. 25 131

    [24]

    Bishop C M, Tipping M E 2000 Proceedings of the 16th Conference Uncertainty in Artificial Intelligence San Francisco, USA, June 30-July 3, 2000 p46

    [25]

    Sun B, Feng H, Zhang Z L 2016 Proceedings of the 41st IEEE International Conference on Acoustics, Speech, and Signal Processing Shanghai, China, March 20-25, 2016 p809

    [26]

    Sun B, Zhang Z L 2015 IEEE Sens. J. 15 7161

    [27]

    Li F, Fang J, Li H, Huang L 2015 IEEE Signal Process. Lett. 22 857

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  • Received Date:  14 March 2017
  • Accepted Date:  15 May 2017
  • Published Online:  05 September 2017

One-bit compressed sensing reconstruction for block sparse signals

    Corresponding author: Sun Biao, sunbiao@tju.edu.cn
  • 1. School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China;
  • 2. Department of Robotics, Ritsumeikan University, Shiga-ken 5258577, Japan
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 61401303, 51578189).

Abstract: Data compression is crucial for resource-constrained signal acquisition and wireless transmission applications with limited data bandwidth. In such applications, wireless data transmission dominates the energy consumption, and the limited telemetry bandwidth could be overwhelmed by the large amount of data generated from multiple sensors. Conventional data compression techniques are computationally intensive, consume large silicon area and offset the energy benefits from reduced data transmission. Recently, compressed sensing (CS) has shown potential in achieving compression performance comparable to previous methods but it has simpler hardware. Especially, one-bit CS theory proves that the signs of compressed measurements contain sufficient information about signal reconstruction, gives that the signals are sparse or compressible in specific dictionaries, thus demonstrating its potential in energy-constrained signal recording and wireless transmission applications. However, the sparsity assumption is too restrictive in many actual scenarios, especially when it is difficult to seek sparse representation for signals. In this paper, a novel one-bit CS method is proposed to reconstruct the signals that are difficult to represent with traditional sparse models. It is capable of recovering signal with comparable compression ratio but avoiding the dictionary selection procedure.The proposed method consists of two parts. 1) The block sparse model is adopted to enforce the structured sparsity of the signals. It not only overcomes the drawbacks of conventional sparse models but also enhances the signal representation accuracy. 2) The probabilistic model of one-bit CS procedure is constructed. Because of the existence of logistic function in probabilistic model of one-bit CS, the Bayesian inference cannot be used to proceed, and the variational Bayesian inference algorithm is developed to reconstruct the original signals from one-bit measurements.Various experiments on different quantities of compressed measurements and iterations are carried out to evaluate the recovery performance of the proposed approach. The photoplethysmography (PPG) signals recorded from subject wrist (dorsal locations) by using PPG sensors built in a wristband are selected as the validation data because they are difficult to represent with traditional sparse dictionaries. The experimental results reveal that the proposed approach outperforms the state-of-the-art one-bit CS method in terms of both reconstruction accuracy and convergence rate.Compared with prior method on one-bit CS, the proposed method shows competitive or superior performance in three aspects. Firstly, by adopting the block sparse model, the proposed method improves the capability to compress signals that are difficult to represent with traditional sparse models, thus making it more practical for long term and real applications. Secondly, by embedding the statistical properties of the one-bit measurements into the recovery algorithm, the proposed method outperforms other one-bit CS methods in terms of both reconstruction performance and convergence speed. Finally, energy and computational efficiency of the proposed method make it an ideal candidate for resource-constrained, large scale, multiple channel signal acquisition and transmission applications.

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