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Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 4314527, 10 pages
https://doi.org/10.1155/2018/4314527
Research Article

Error in the Reconstruction of Nonsparse Images

1Faculty of Electrical Engineering, University of Montenegro, 81000 Podgorica, Montenegro
2GIPSA Lab, INP, University Grenoble Alpes, 38400 Saint-Martin-d’Hères, France

Correspondence should be addressed to Miloš Daković; em.ca@solim

Received 31 August 2017; Revised 9 December 2017; Accepted 28 December 2017; Published 12 February 2018

Academic Editor: Joan Serra-Sagrista

Copyright © 2018 Miloš Brajović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. L. Donoho, “Compressed sensing,” Institute of Electrical and Electronics Engineers Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. E. J. Candès, “The restricted isometry property and its implications for compressed sensing,” Comptes Rendus Mathematique, vol. 346, no. 9-10, pp. 589–592, 2008. View at Publisher · View at Google Scholar · View at Scopus
  3. R. G. Baraniuk, “Compressive sensing,” IEEE Signal Processing Magazine, vol. 24, no. 4, pp. 118–121, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” Institute of Electrical and Electronics Engineers Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  5. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling: a sensing/sampling paradigm that goes against the common knowledge in data acquisition,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. B. Wohlberg, “Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem,” IEEE Transactions on Signal Processing, vol. 51, no. 12, pp. 3053–3060, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. L. Stanković, S. Stanković, and M. Amin, “Missing samples analysis in signals for applications to L-estimation and compressive sensing,” Signal Processing, vol. 94, no. 1, pp. 401–408, 2014. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Stanković, I. Stanković, and M. Daković, “Nonsparsity influence on the ISAR recovery from reduced data,” IEEE Transactions on Aerospace and Electronic Systems, vol. 52, no. 6, pp. 3065–3070, 2016. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Stanković, I. Orović, and L. Stanković, “An automated signal reconstruction method based on analysis of compressive sensed signals in noisy environment,” Signal Processing, vol. 104, pp. 43–50, 2014. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer, Berlin, Germany, 2010. View at Publisher · View at Google Scholar · View at Scopus
  11. M. A. Davenport, M. F. Duarte, Y. C. Eldar, and G. Kutyniok, “Compressed sensing: Theory and applications,” in Introduction to compressed sensing, Cambridge University Press, Cambridge, UK, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. Needell and J. A. Tropp, “CoSaMP: Iterative signal recovery from incomplete and inaccurate samples,” Applied and Computational Harmonic Analysis , vol. 26, no. 3, pp. 301–321, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. E. Sejdić, M. A. Rothfuss, M. L. Gimbel, and M. H. Micklel, “Comparative analysis of compressive sensing approaches for recovery of missing samples in implantable wireless Doppler device,” IET Signal Processing, vol. 8, no. 3, pp. 230–238, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. E. Sejdić, A. Can, L. F. Chaparro, C. M. Steele, and T. Chau, “Compressive sampling of swallowing accelerometry signals using time-frequency dictionaries based on modulated discrete prolate spheroidal sequences,” EURASIP Journal on Advances in Signal Processing, vol. 2012, article 101, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. E. Sejdić, “Time-frequency compressive sensing,” in Time-Frequency Signal Analysis and Processing, B. Boashash, Ed., pp. 424–429, Academic Press, Mass, USA.
  16. B. Jokanović, M. G. Amin, Y. D. Zhang, and F. Ahmad, “Multi-window time-frequency signature reconstruction from undersampled continuous-wave radar measurements for fall detection,” IET Radar, Sonar & Navigation, vol. 9, no. 2, pp. 173–183, 2015. View at Publisher · View at Google Scholar · View at Scopus
  17. Z. Zhang, Y. Xu, J. Yang, X. Li, and D. Zhang, “A survey of sparse representation: algorithms and applications,” IEEE Access, vol. 3, pp. 490–530, 2015. View at Publisher · View at Google Scholar
  18. I. Volaric and V. Sucic, “On the noise impact in the L1 based reconstruction of the sparse time-frequency distributions,” in Proceedings of the 1st International Conference on Broadband Communications for Next Generation Networks and Multimedia Applications, (CoBCom '16), Graz, Austria, September 2016. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Stanković, I. Orović, S. Stanković, and M. G. Amin, “Robust time frequency analysis based on the L-estimation and compressive sensing,” IEEE Signal Processing Letters, vol. 20, no. 5, pp. 499–502, 2013. View at Publisher · View at Google Scholar · View at Scopus
  20. L. Stanković, M. Daković, and S. Vujović, “Reconstruction of sparse signals in impulsive disturbance environments,” Circuits, Systems and Signal Processing, vol. 36, no. 2, pp. 767–794, 2017. View at Publisher · View at Google Scholar
  21. X. Li and G. Bi, “Image reconstruction based on the improved compressive sensing algorithm,” in Proceedings of the IEEE International Conference on Digital Signal Processing, (DSP '15), pp. 357–360, Singapore, July 2015. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Musić, T. Marasović, V. Papić, I. Orović, and S. Stanković, “Performance of compressive sensing image reconstruction for search and rescue,” IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 11, pp. 1739–1743, 2016. View at Publisher · View at Google Scholar
  23. I. Stanković, I. Orović, M. Daković, and S. Stanković, “Denoising of sparse images in impulsive disturbance environment,” Multimedia Tools and Applications. View at Publisher · View at Google Scholar
  24. L. Stanković, “Digital Signal Processing with Selected Topics, CreateSpace Independent Publishing Platform, An Amazon.com Company”.
  25. P. Maechler, C. Studer, D. E. Bellasi et al., “VLSI design of approximate message passing for signal restoration and compressive sensing,” IEEE Journal on Emerging and Selected Topics in Circuits and Systems, vol. 2, no. 3, pp. 579–590, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. G. Bi, S. K. Mitra, and S. Li, “Sampling rate conversion based on DFT and DCT,” Signal Processing, vol. 93, no. 2, pp. 476–486, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. V. Britanak and K. R. Rao, “Efficient implementation of the forward and inverse MDCT in MPEG audio coding,” IEEE Signal Processing Letters, vol. 8, no. 2, pp. 48–51, 2001. View at Publisher · View at Google Scholar · View at Scopus
  28. J. J. More and G. Toraldo, “On the solution of large quadratic programming problems with bound constraints,” SIAM Journal on Optimization, vol. 1, no. 1, pp. 93–113, 1991. View at Publisher · View at Google Scholar · View at MathSciNet
  29. G. Davis, S. Mallat, and M. Avellaneda, “Adaptive greedy approximations,” Constructive Approximation. An International Journal for Approximations and Expansions, vol. 13, no. 1, pp. 57–98, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  30. R. Tibshirani, “Regression shrinkage and selection via the lasso: a retrospective,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol. 73, no. 3, pp. 273–282, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus