Skip to main content
SpringerLink
Log in

Foveated Compressed Sensing

  • Short Paper
  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Combining the principles behind Compressed Sensing theory with a wavelet-based implementation of a foveation operator inspired by the human visual system yields significant compression performances on both 1D and 2D signals. The solution provides spatially variable quality of the reconstructed information, enabling better approximation on specific regions of interest. Four distinct algorithms are compared in terms of reconstruction error and compression ratio on a set of ECG records and natural images.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. R.G. Baraniuk, V. Cevher, M.F. Duarte, C. Hegde, Model-based compressive sensing. IEEE Trans. Inf. Theory 56, 1982–2001 (2010)

    Article  MathSciNet  Google Scholar 

  2. R. Benzid, E. Marir, A. Boussaad, M. Benyoucef, D. Arar, Fixed percentage of wavelet coefficients to be zeroed for ECG compression. Electron. Lett. 39, 830–831 (2003)

    Article  Google Scholar 

  3. E.J. Candes, T. Plan, A probabilistic and RIPless theory of compressed sensing. IEEE Trans. Inf. Theory 57, 7235–7254 (2011)

    Article  MathSciNet  Google Scholar 

  4. E.C. Chang, S. Mallat, C. Yap, Wavelet foveation. J. Appl. Comput. Harmon. Anal. 9, 312–335 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. C. Chen, J. Huang, Compressive Sensing MRI with Wavelet Tree Sparsity, in Proceedings Neural Information Processing Systems (2012), pp. 1124–1132

  6. I.B. Ciocoiu, Foveated compressed sensing, in Proceedings od the European Conference on Circuit Theory and Design (2011), pp. 29–32

  7. D. Donoho, Y. Tsaig, I. Drori, J. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit (Stanford University, Technical Report, 2006)

  8. J. Huang, T. Zhang, T. Metaxas, Learning with structured sparsity. J. Mach. Learn. Res. 12, 3371–3412 (2011)

    MATH  MathSciNet  Google Scholar 

  9. J. Huang, S. Zhang, D. Metaxas, Efficient MR image reconstruction for compressed MR imaging. Med. Image Anal. 15, 670–679 (2011)

    Article  Google Scholar 

  10. S. Kadambe, R. Murray, F. Boudreaux-Bartels, Wavelet transform-based QRS complex detector. IEEE Trans. Biomed. Eng. 46, 838–847 (1999)

    Article  Google Scholar 

  11. R. Larcom, T.R. Coffman, Foveated image formation through compressive sensing, in Proceedings of the IEEE Southwest Symposium Image Analysis and Interpretation (2010), pp. 145–148

  12. S. Lee, A. Bovik, B. Evans, Efficient implementation of foveation filtering, in Proceeidngs of TI DSP Educators Conference (1999)

  13. M.S. Lewicki, T.J. Sejnowski, Learning overcomplete representations. Neural Comput. 12, 337–365 (2000)

    Article  Google Scholar 

  14. D.G. Lowe, Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60, 91–110 (2004)

    Article  Google Scholar 

  15. Z. Lu, D.Y. Kim, W.A. Pearlman, Wavelet compression of ECG signals by the set partitioning in hierarchical trees algorithm. IEEE Trans. Biomed. Eng. 47, 849–56 (2000)

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. S.G. Mallat, S. Zhong, Characterization of signals from multiscale edges. IEEE Trans. Pattern Anal. Mach. Intell. 14, 710–732 (1992)

    Article  Google Scholar 

  18. B.A. Olshausen, D.J. Field, Natural image statistics and efficient coding. Network 7, 333–339 (1996)

    Article  Google Scholar 

  19. PhysioBank, physiologic signal archives for biomedical research. http://www.physionet.org/physiobank/

  20. J.M. Shapiro, Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. Signal Process. 41(1993), 3445–3462 (1993)

    Article  MATH  Google Scholar 

  21. Y. Tsaig, D. Donoho, Extensions of compressed sensing. Signal Proc. 86, 549–571 (2006)

    Article  MATH  Google Scholar 

  22. M. F. Valstar, B. Martinez, X. Binefa, M. Pantic, Facial point detection using boosted regression and graph models, in Proceedings IEEE International Conference on Computer Vision and Pattern Recognition (2010), pp. 2729–2736

  23. Y. Yu, B. Wang, L. Zhang, Saliency-based compressive sampling for image analysis. IEEE Signal Proc. Lett. 17, 973–976 (2010)

    Article  Google Scholar 

  24. Y. Zhang, Theory of compressive sensing via L1 minimization: a non-rip analysis and extensions (Rice University, Technical Report, 2008)

  25. Z. Zhang, B.D. Rao, Extension of SBL algorithms for the recovery of block sparse signals with intra-block correlation. IEEE Trans Signal Proc. 61(8), 2009–2015 (2013)

    Article  Google Scholar 

  26. Y. Zigel, A. Cohen, A. Katz, The weighted diagnostic distortion (WDD) measure for ECG signal compression. IEEE Trans. Biomed. Eng. 47, 1422–1430 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Electronics, Telecommunications and Information Technology, “Gheorghe Asachi” Technical University of Iasi, Iasi, Romania

    Iulian B. Ciocoiu

Authors
  1. Iulian B. Ciocoiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iulian B. Ciocoiu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ciocoiu, I.B. Foveated Compressed Sensing. Circuits Syst Signal Process 34, 1001–1015 (2015). https://doi.org/10.1007/s00034-014-9878-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-014-9878-2

Keywords

Search

Navigation