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Multimedia Tools and Applications

, Volume 75, Issue 5, pp 2565–2578 | Cite as

Compressive sensing reconstruction for compressible signal based on projection replacement

  • Zan Chen
  • Xingsong Hou
  • Chen Gong
  • Xueming Qian
Article

Abstract

Compressive sensing can reconstruct compressible or sparse signal at the under-sampling rate. However small coefficients of the compressible signal with large number but low energy are hard to be reconstructed, while also infect the accuracy of the big coefficients. In this reason, for the compressive sensing algorithms such as orthogonal match pursuit (OMP) and tree-structed wavelet compressive sensing (TSW-CS), an assumed error is in the measurement model, which makes the reconstructed results not satisfy the original measurement model. Aiming at this problem, we propose the projection replacement (PR) algorithm by building the measurement space and its orthogonal complement space with singular value decomposition, and replacing the projection in measurement space of the reconstructed result with the pseudo-inverse one. The proposed PR algorithm eliminates the hypothetic measurement error in OMP and TSW-CS reconstructed model, and it guarantees theoretically that the PR results have a smaller error. Its effectiveness is verified experimentally with OMP and TSW-CS. The proposed algorithm serves as a good reconstruction algorithm for the CS-based applications such as image coding, super-resolution, video retrieval etc.

Keywords

Compressive sensing Orthogonal projection TSW-CS OMP 

Notes

Acknowledgments

This work was supported by National Natural Science Foundation of China (No.61373113) and the Fundamental Research for the Central University (No.xjj2012023).

References

  1. 1.
    Cands EJ (2006) Compressive sampling. In: Proceedings of the international congress of mathematics, vol 3, pp 1433–1452Google Scholar
  2. 2.
    Deng CW, Lin WS, Lee B-S, Lau CT (2012) Robust image coding based upon compressive sensing. IEEE Trans Multimed 14(2):278–290CrossRefGoogle Scholar
  3. 3.
    Donoho D L (2006) Compressive sensing. IEEE Trans Inf Theory 52(4):1289–1360MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Fannjiang A, Liao W (2012) Super-resolution by compressive sensing algorithms. In: IEEE Proceeding Asilomar conference on signals, systems and computers, pp 411–415Google Scholar
  5. 5.
    Golub GH, Loan CFV (2013) Matrix computation, 4th edn. John Hopkins University Press, MarylandzbMATHGoogle Scholar
  6. 6.
    He L, Carin L (2009) Exploiting structure in wavelet-based Bayesian compressive sensing. IEEE Trans Signal Process 57(9):3488–3497MathSciNetCrossRefGoogle Scholar
  7. 7.
    He L, Chen H, Carin L (2010) Tree-structed compressive sensing with variational Bayesian analysis. IEEE Signal Process Letters 17(3):233–236CrossRefGoogle Scholar
  8. 8.
    Hou XS, Yang J, Jiang GF, Qian XM (2013) Complex SAR image compression based on directional lifting wavelet transform with high clustering capability. IEEE Trans Geosci Remote Sensing 51 (1):527–538CrossRefGoogle Scholar
  9. 9.
    Ji S, Xue Y, Carin L (2008) Bayesian compressive sensing. IEEE Trans Signal Process 56(6):2346–2356MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kulkarin N, Nagesh P, Gowda R, Li BX (2011) Understanding compressive sensing and sparse representation-based super-resolution. IEEE Trans Circuits Syst Video Technol 22(5):778–789CrossRefGoogle Scholar
  11. 11.
    Liu LW, Wang LH, Zhang M (2014) Depth map super-resolution based on joint dictionary learning. Multimed Tools Appl. doi: 10.1007/s11042-014-2002-6
  12. 12.
    Mallat SG, Zhang Z (1993) Matching pursuits with time-frequency dictionaries. IEEE Trans Signal Process 41(3):3397–3415CrossRefzbMATHGoogle Scholar
  13. 13.
    Ruiz P, Babacan SD, Gao L, Li Z (2011) Video retrieval suing sparse Bayesian reconstruction. In: 2011 IEEE international conference on multimedia and expo, pp 1-6Google Scholar
  14. 14.
    Tropp JA, Gilbert AC (2007) Signal recover from random measurement via orthogonal matching pursuit. IEEE Trans Inf Theory 53(12):4655–4666MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Wang LJ, Wu XL, Shi GM (2008) A compressive sensing approach of multiple descriptions for network multimedia communication. In: Processing IEEE workshop multimedia signal process, vol 1, pp 445–449Google Scholar
  16. 16.
    Xu L, Liang Q (2010) Compressive sensing using singular value decomposition. In: Lecture notes in computer science, vol 6221, pp 338–342Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Zan Chen
    • 1
  • Xingsong Hou
    • 1
  • Chen Gong
    • 2
  • Xueming Qian
    • 1
  1. 1.School of Electronic and Information EngineeringXi’an JiaoTong UniversityXianChina
  2. 2.School of Electronic and Information EngineeringUniversity of Science and Technology of ChinaHefeiChina

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