Skip to main content
SpringerLink
Log in

Analysis of the Orthogonal Matching Pursuit Algorithm with Prior Information

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

Compressed sensing uses a small amount of compressed data to represent high dimensional data, where the reconstruction algorithm is one of the main research topics. Among various algorithms, orthogonal matching pursuit (OMP) recovers the original signals in a greedy manner. Recently, the performance bound of OMP algorithm has been widely investigated. In this paper, we study OMP algorithm in the scenario that the decoder has the support probability vector, which can be used as prior information for recovery. We develop the relationship between the restricted isometry property (RIP) constant \(\delta _{K + 1}\) and prior information. Based on the RIP results, some special cases that are further discussed to provide a deeper understanding of the relationship. The derived results show that the effective prior information is useful for relaxing the performance bound of the RIP isometry \(\delta _{K + 1}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Figueiredo, M. A. T., Nowak, R. D., & Wright, S. J. (2007). Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE Journal of Selected Topics in Signal Processing, 1(4), 586–597.

    Article  Google Scholar 

  3. Chen, S. S., Donoho, D. L., & Saunders, M. A. (2001). Atomic decomposition by basis pursuit. SIAM Review, 43(1), 129–159.

    Article  MathSciNet  MATH  Google Scholar 

  4. Kaasschieter, E. F. (1988). Preconditioned conjugate gradients for solving singular systems. Journal of Computational and Applied Mathematics, 24(1–2), 265–275.

    Article  MathSciNet  MATH  Google Scholar 

  5. Pati, Y. C., Rezaiifar, R., & Krishnaprasad, P. S. (1993). Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. Conference record of the 27th Asilomar conference on signals, systems and computers (Vol. 1, pp. 40–44).

  6. Tropp, J. (2004). Greed is good: Algorithmic results for sparse approximation. IEEE Transactions on Information Theory, 50(10), 2231–2242.

    Article  MathSciNet  MATH  Google Scholar 

  7. Needell, D., & Tropp, J. A. (2010). CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Communications of the ACM, 53(12), 93–100.

    Article  MATH  Google Scholar 

  8. Xu, W., Tian, Y., & Lin, J. (2013). Partial segmented compressed sampling for analog-to-information conversion. AEU - International Journal of Electronics and Communications, 67(2), 294–296.

    Article  Google Scholar 

  9. Candes, E. J. (2008). The restricted isometry property and its implications for compressed sensing. Comptes Rendus Mathematique, 346(9–10), 589–592.

    Article  MathSciNet  MATH  Google Scholar 

  10. Davenport, M. A., & Wakin, M. B. (2010). Analysis of orthogonal matching pursuit using the restricted isometry property. IEEE Transactions on Information Theory, 56(9), 4395–4401.

    Article  MathSciNet  MATH  Google Scholar 

  11. Huang, S., & Zhu, J. (2011). Recovery of sparse signals using OMP and its variants: Convergence analysis based on RIP. Inverse Problems, 27(3), 035003.

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, E., & Temlyakov, V. N. (2012). The orthogonal super greedy algorithm and applications in compressed sensing. IEEE Transactions on Information Theory, 58(4), 2040–2047.

    Article  MathSciNet  MATH  Google Scholar 

  13. Mo, Q., & Shen, Y. (2012). A remark on the restricted isometry property in orthogonal matching pursuit. IEEE Transactions on Information Theory, 58(6), 3654–3656.

    Article  MathSciNet  MATH  Google Scholar 

  14. Maleh. R. (2011). Improved RIP analysis of orthogonal matching pursuit, [Online]. Available: http://arxiv.org/ftp/arxiv/papers/1102/1102.4311.pdf

  15. Dai, W., & Milenkovic, O. (2009). Subspace pursuit for compressive sensing: Closing the gap between performance and complexity. IEEE Transactions on Information Theory, 55(5), 2230–2249.

    Article  MathSciNet  MATH  Google Scholar 

  16. Chang, L., & Wu, W. (2014). An improved RIP-based performance guarantee for sparse signal recovery via orthogonal matching pursuit. In 2014 6th international symposium on communications, control and signal processing (ISCCSP) (pp. 28–31).

  17. Chang, L., & Wu, W. (2014). An improved RIP-based performance guarantee for sparse signal recovery via orthogonal matching pursuit. IEEE Transactions on Information Theory, 60(9), 5702–5715.

    Article  MathSciNet  MATH  Google Scholar 

  18. Xu, W., Lin, J., Niu, K., He, Z., & Wang, Y. (2014). Performance analysis of partial support recovery and signal reconstruction of compressed sensing. Signal Processing, IET, 8(2), 188–201.

    Article  Google Scholar 

  19. Scarlett, J., Evans, J. S., & Dey, S. (2013). Compressed sensing with prior information: Information-theoretic limits and practical decoders. IEEE Transactions on Signal Processing, 61(2), 427–439.

    Article  MathSciNet  Google Scholar 

  20. Eldar, Y. C., Kuppinger, P., & Bolcskei, H. (2010). Compressed sensing of block-sparse signals: Uncertainty relations and efficient recovery. IEEE Transactions on Signal Processing, 58(6), 3042–3054.

    Article  MathSciNet  Google Scholar 

  21. Yu, X., & Baek, S. J. (2013). Sufficient conditions on stable recovery of sparse signals with partial support information. IEEE Transactions on Signal Processing Letters, 20(5), 539–542.

    Article  Google Scholar 

  22. Friedlander, M. P., Mansour, H., Saab, R., & Yilmaz, O. (2012). Recovering compressively sampled signals using partial support information. IEEE Transactions on Information Theory, 58(2), 1122–1134.

    Article  MathSciNet  MATH  Google Scholar 

  23. Miosso, C. J., Borries, R. V., & Pierluissi, J. H. (2013). Compressive sensing with prior information: Requirements and probabilities of reconstruction in l1-minimization. IEEE Transactions on Signal Processing, 61(9), 2150–2164.

    Article  MathSciNet  Google Scholar 

  24. Friedlander, M. P., Mansour, H., Saab, R., & Yilmaz, O. (2012). Recovering compressively sampled signals using partial support information. IEEE Transactions on Information Theory, 58(2), 1122–1134.

    Article  MathSciNet  MATH  Google Scholar 

  25. Khajehnejad, M. A., Xu, W., Avestimehr, A. S., & Hassibi, B. (2011). Analyzing weighted minimization for sparse recovery with nonuniform sparse models. IEEE Transactions on Signal Processing, 59(5), 1985–2001.

    Article  MathSciNet  Google Scholar 

  26. Khajehnejad, M. A., Xu, W., Avestimehr, A. S., & Hassibi, B. (2010). Improved sparse recovery thresholds with two-step reweighted minimization. In IEEE international symposium on information theory (pp. 1603–1607).

  27. Lu, W., & Vaswani, N. (2009). Modified compressive sensing for real-time dynamicMRimaging. IEEE International Conference on Image Processing (ICIP) (pp. 3045–3048).

  28. Coates, J., Pointurier, Y., & Rabbat, M. (2007). Compressed network monitoring. In IEEE Workshop on Statistical Signal Processing (pp. 418–422).

  29. Milenkovic, O., Baraniuk, R., & Simunic-Rosing, T. (2007). Compressed sensing meets bionformatics: A new DNA microarray architecture. In Information theory and applications workshop. San Diego.

  30. Erickson, S., & Sabatti, C. (2005). Empirical Bayes estimation of a sparse vector of gene expression changes. Statistical Applications in Genetics and Molecular Biology, 4(1), doi:10.2202/1544-6115.1132.

  31. Parvaresh, F., Vikalo, H., Misra, S., & Hassibi, B. (2008). Recovering sparse signals using sparse measurement matrices in compressed DNA microarrays. IEEE Journal of Selected Topics in Signal Processing, 2(3), 275–285.

    Article  Google Scholar 

  32. Han, Y., Zhao, P., Sui, L., & Fan, Zhenkai (2014). Time-varying channel estimation based on dynamic compressive sensing for OFDM systems. In 2014 IEEE International Symposium on Broadband Multimedia Systems and Broadcasting (BMSB) (pp. 1–5).

  33. Pudlewski, S., Prasanna, A., & Melodia, T. (2012). Compressed-sensing-enabled video streaming for wireless multimedia sensor networks. IEEE Transactions on Mobile Computing, 11(6), 1060–1072.

    Article  Google Scholar 

  34. Liu, Z., Elezzabi, A. V., & Zhao, H. V. (2011). Maximum frame rate video acquisition using adaptive compressed sensing. IEEE Transactions on Circuits and Systems for Video Technology, 21(11), 1704–1718.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Beijing University of Posts and Telecommunications, No. 10 Xitucheng Road, Haidian district, Beijing, China

    Zhilin Li, Wenbo Xu, Yupeng Cui & Jiaru Lin

Authors
  1. Zhilin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenbo Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yupeng Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiaru Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhilin Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Z., Xu, W., Cui, Y. et al. Analysis of the Orthogonal Matching Pursuit Algorithm with Prior Information. Wireless Pers Commun 96, 1495–1506 (2017). https://doi.org/10.1007/s11277-017-4252-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-017-4252-x

Keywords

Search

Navigation