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A New Bayesian Method for Jointly Sparse Signal Recovery

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Neural Information Processing (ICONIP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10637))

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Abstract

In this paper, we address the recovery of a set of jointly sparse vectors from incomplete measurements. We provide a Bayesian inference scheme for the multiple measurement vector model and develop a novel method to carry out maximum a posteriori estimation for the Bayesian inference based on the prior information on the sparsity structure. Instead of implementing Bayesian variables estimation, we establish the corresponding minimization algorithms for all of the sparse vectors by applying block coordinate descent techniques, and then solve them iteratively and sequently through a re-weighted method. Numerical experiments demonstrate the enhancement of joint sparsity via the new method and its robust recovery performance in the case of a low sampling ratio.

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References

  1. Candès, E.J., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Lustig, M., Donoho, D., Pauly, J.M.: Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58(6), 1182–1195 (2007)

    Article  Google Scholar 

  3. Candès, E.J., Tao, T.: Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inf. Theory 52(12), 5406–5425 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bajwa, W., Haupt, J., Sayeed, A., Nowak, R.: Compressive wireless sensing. In: Proceedings of the 5th International Conference on Information Processing in Sensor Networks, pp. 134–142. ACM (2006)

    Google Scholar 

  5. Gorodnitsky, I.F., Rao, B.D.: Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600–616 (2002)

    Article  Google Scholar 

  6. Petre, S., Randolph, M.: Spectral analysis of signals (POD). Leber Magen Darm 13(2), 57–63 (2005)

    Google Scholar 

  7. Cotter, S.F., Rao, B.D., Engan, K., Kreutz-Delgado, K.: Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Trans. Signal Process. 53(7), 2477–2488 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Eldar, Y.C., Mishali, M.: Robust recovery of signals from a structured union of subspaces. IEEE Trans. Inf. Theory 55(11), 5302–5316 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Eldar, Y.C., Rauhut, H.: Average case analysis of multichannel sparse recovery using convex relaxation. IEEE Trans. Inf. Theory 56(1), 505–519 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Davies, M.E., Eldar, Y.C.: Rank awareness in joint sparse recovery. IEEE Trans. Inf. Theory 58(2), 1135–1146 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lee, K., Bresler, Y., Junge, M.: Subspace methods for joint sparse recovery. IEEE Trans. Inf. Theory 58(6), 3613–3641 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  12. Blanchard, J.D., Davies, M.E.: Recovery guarantees for rank aware pursuits. IEEE Signal Process. Lett. 19(7), 427–430 (2012)

    Article  Google Scholar 

  13. Gogna, A., Shukla, A., Agarwal, H.K., Majumdar, A.: Split Bregman algorithms for sparse/joint-sparse and low-rank signal recovery: application in compressive hyperspectral imaging. In: IEEE International Conference on Image Processing, pp. 1302–1306 (2015)

    Google Scholar 

  14. Kim, J.M., Lee, O.K., Ye, J.C.: Compressive MUSIC: revisiting the link between compressive sensing and array signal processing. IEEE Trans. Inf. Theory 58(1), 278–301 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Vila, J.P., Schniter, P.: Expectation-maximization Gaussian-mixture approximate message passing. IEEE Trans. Signal Process. 61(19), 4658–4672 (2013)

    Article  MathSciNet  Google Scholar 

  16. Li, L., Huang, X., Suykens, J.A.K.: Signal recovery for jointly sparse vectors with different sensing matrices. Signal Process. 108(C), 451–458 (2015)

    Article  Google Scholar 

  17. Candès, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted \(\ell _1\) minimization. J. Fourier Anal. Appl. 14(5), 877–905 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ji, S., Dunson, D., Carin, L.: Multitask compressive sensing. IEEE Trans. Signal Process. 57(1), 92–106 (2009)

    Article  MathSciNet  Google Scholar 

  19. George, E.I., Mcculloch, R.E.: Approaches for Bayesian variable selection. Stat. Sin. 7(2), 339–373 (1997)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, China

    Haiyan Yang, Xiaolin Huang, Cheng Peng & Jie Yang

  2. Department of Automation, Tsinghua University, Beijing, China

    Li Li

Authors
  1. Haiyan Yang
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  2. Xiaolin Huang
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  3. Cheng Peng
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  4. Jie Yang
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  5. Li Li
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Corresponding author

Correspondence to Xiaolin Huang .

Editor information

Editors and Affiliations

  1. Guangdong University of Technology, Guangzhou, China

    Derong Liu

  2. Guangdong University of Technology, Guangzhou, China

    Shengli Xie

  3. South China University of Technology, Guangzhou, China

    Yuanqing Li

  4. Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Dongbin Zhao

  5. King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    El-Sayed M. El-Alfy

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Yang, H., Huang, X., Peng, C., Yang, J., Li, L. (2017). A New Bayesian Method for Jointly Sparse Signal Recovery. In: Liu, D., Xie, S., Li, Y., Zhao, D., El-Alfy, ES. (eds) Neural Information Processing. ICONIP 2017. Lecture Notes in Computer Science(), vol 10637. Springer, Cham. https://doi.org/10.1007/978-3-319-70093-9_94

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  • DOI: https://doi.org/10.1007/978-3-319-70093-9_94

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70092-2

  • Online ISBN: 978-3-319-70093-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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