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Structural Scrambling of Circulant Matrices for Cost-effective Compressive Sensing

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Abstract

Compressed sensing (CS) is a promising theory that is able to measure signal below the Nyquist rate through measurement matrices. Random matrices are regarded as optimal measurement matrices to spread out signals to a small number of measurements. However, the random matrices cost too much memory space for implementation. The structured matrices are then proposed to reduce such enormous memory cost. Nevertheless, the recovery performance of the structured matrices suffers from severe degradation. In this paper, we propose sign-flipped scrambling method and extended-select scrambling method for circulant matrices to compensate the performance loss. The sign-flipped scrambling for circulant matrices is able to approach recovery performance of random matrices within defined guarantee region. On the other hand, the extended-select scrambling together with sign-flipped scrambling for circulant matrices is able to approximate the overall recovery performance of the random matrices. In addition, architectures are designed to realize the proposed scrambling methods. Compared with random matrices, proposed scrambling matrices are more cost-effective for implementation.

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References

  1. Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.

    Article  MathSciNet  MATH  Google Scholar 

  2. Baraniuk, R. G. (2007). Compressive sensing. IEEE Signal Processing Magazine, 24(4), 118–122.

    Article  MathSciNet  Google Scholar 

  3. Lustig, M., Donoho, D., & Pauly, J. (2007). Sparse MRI: the application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine, 58(6), 1182–1195.

    Article  Google Scholar 

  4. Jiang, W. & Yang, J. (2016). The rate-distortion optimized compressive sensing for image coding. Journal of Signal Processing System. [Online], pp. 1–13. Available: http://link.springer.com/article/10.1007%2Fs11265-015-1087-0.

  5. Chen, C. Y., Wu, W. R., Gau, C. S. (2015). Joint AoA and channel estimation for SIMO-OFDM systems: a compressive-sensing approach. Journal Of Signal Processing System. [Online], pp. 1–15. Available: http://link.springer.com/article/10.1007%2Fs11265-015-1043-z.

  6. Pfetsch, S, Ragheb, T, Laska, J, Nejati, H, Gilbert, A, Strauss, M, Baraniuk R, & Massoud, Y. (2008). On the feasibility of hardware implementation of sub-Nyquist random-sampling based analog-to-information conversion. Proceeding of IEEE International Symposium on Circuits and Systems, 1480–1483.

  7. Chen, X., Yu, Z., Hoyos, S., Sadler, B. M., & Silva-Martinez, J. (2010). A sub-Nyquist rate sampling receiver exploiting compressive sensing. IEEE Transactions on Circuits System I, 58(3), 507–520.

    Article  MathSciNet  Google Scholar 

  8. Bajwa, W. U., Haupt, J.D., Raz, G. M., Wright, S.J. & Nowak, R. D. (2007). Toeplitz-structures compressed sensing matrices. Proceedings of IEEE/SP Workshop Statistics. Signal Process, 294–298.

  9. Yin, W., Morgan, S. P., Yang, J. & Zhang, Y. (2010). Practical compressive sensing with Toeplitz and circulant matrices. Rice Univ., Houston, TX, CAAM Tech. Rep. TR10-01.

  10. Tropp, J., & Gilbert, A. (2007). Signal recovery from random measurements via orthogonal matching pursuit. IEEE Transactions on Information Theory, 53(12), 4655–4666.

    Article  MathSciNet  MATH  Google Scholar 

  11. Duarte, M. F., & Eldar, Y. C. (2011). Structured compressed sensing: from theory to applications. IEEE Transactions on Signal Processing, 59(9), 4053–4085.

    Article  MathSciNet  Google Scholar 

  12. Candes, E. J., & Tao, T. (2006). Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Transactions on Information Theory, 52(12), 5406–5425.

    Article  MathSciNet  MATH  Google Scholar 

  13. Rauhut, H., Romberg, J. K., & Tropp, J. A. (2012). Restricted isometries for partial random circulant matrices. Applied and Computational Harmonic Analysis, 32(2), 242–254.

    Article  MathSciNet  MATH  Google Scholar 

  14. Allstot, E. G., Chen, A. Y.,Dixon, A. M. R., Gangopadhyay, D. & Allstot, D. J. (2010). Compressive sampling of ECG bio-signals: quantization noise and sparsity considerations. Proceedings of IEEE Biomedical Circuits and System Conference, 41–44.

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Acknowledgments

This work was financially supported in part by the Ministry of Science and Technology of Taiwan under Grants MOST 103-2622-E-002-034 & 104-2622-8-002-002, which are sponsored by MediaTek Inc., Hsin-chu, Taiwan, and NOVATEK Fellowship. Part of the technical contents in this paper was presented in part at the IEEE SiPS, Hangzhou, China, Oct. 2015.

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Authors and Affiliations

  1. Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, 10617, Taiwan, Republic of China

    Yu-Min Lin & An-Yeu (Andy) Wu

  2. Department of Electrical Engineering, National Taiwan University, Taipei, 10617, Taiwan, Republic of China

    Jie-Fang Zhang & Jing Geng

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  1. Yu-Min Lin
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  2. Jie-Fang Zhang
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  4. An-Yeu (Andy) Wu
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Correspondence to Yu-Min Lin.

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Lin, YM., Zhang, JF., Geng, J. et al. Structural Scrambling of Circulant Matrices for Cost-effective Compressive Sensing. J Sign Process Syst 90, 695–707 (2018). https://doi.org/10.1007/s11265-016-1189-3

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  • DOI: https://doi.org/10.1007/s11265-016-1189-3

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