Skip to main content
Log in

Nonlocally Adaptive Pattern Classification Based Compressed Sensing for Video Recovery

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

Abstract

Traditional video coding algorithms usually undergo several coding steps for each frame before transmission, which reduces the efficiency at the encoder. The compressed sensing (CS) as an innovative method in signal processing can make the encoder much easier than ever before, with which each frame only needs to multiply a projection matrix at the encoder, if the frame is sparse in a transform domain. Frames in a video usually exhibit sparsity in different parts on different bases; however, existing compressed sensing reconstruction methods usually recover a frame in a fixed set of bases for the entirety of the frame. Therefore, the frames cannot be recovered faithfully by the conventional CS reconstruction methods from a small number of measurements. In this paper, in order to rectify the flaw, we construct an initial estimation frame by motion estimation from neighboring frames and through the observation of the current frame. Then, nonlocally adaptive sparse signal presentation facilitation by a 2D piecewise autoregressive (AR) model is integrated into the reconstruction. The piecewise AR model is generated from the pattern classification of subimages of the initial estimation frame and its neighboring frames. An iterative procedure is proposed to recover a new estimated frame and its AR model alternatively, until the termination threshold is satisfied. The experimental results demonstrating the capabilities of the proposed method are presented.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

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(4), 1982–2001 (2010)

    Article  MathSciNet  Google Scholar 

  2. S.P. Boyd, L. Vandenberghe, Convex Optimization (Cambridge Univ. Press, Cambridge, 2004)

    Book  MATH  Google Scholar 

  3. E.J. Candès, The restricted isometry property and its implications for compressed sensing. C. R. Math. 346(9–10), 589–592 (2008)

    Article  MATH  Google Scholar 

  4. E.J. Candès, T. Tao, Decoding by linear programming. IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. E.J. Candès, J.K. Romberg, T. Tao, Stable signal recovery from incomplete and inaccurate measurements. Commun. Pure Appl. Math. 59(8), 1207–1223 (2006)

    Article  MATH  Google Scholar 

  7. T.T. Do, Y. Chen, D.T. Nguyen, N. Nguyen, L. Gan, T.D. Tran, in Distributed Compressed Video Sensing, 16th IEEE International Conference on Image Processing (ICIP) (2009), pp. 1393–1396

    Google Scholar 

  8. D.L. Donoho, Compressed sensing. IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  9. M.A.T. Figueiredo, R.D. Nowak, S.J. Wright, Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007)

    Article  Google Scholar 

  10. J. Haupt, R. Baraniuk, R. Castro, R. Nowak, Sequentially Designed Compressed Sensing, Statistical Signal Processing Workshop (SSP) (IEEE, New York, 2012), pp. 401–404

    Google Scholar 

  11. S.J. Kim, K. Koh, M. Lustig, S. Boyd, D. Gorinevsky, An interior-point method for large-scale l1-regularized least squares. IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007)

    Article  Google Scholar 

  12. C. Li, H. Jiang, P. Wilford, Y. Zhang, M. Scheutzow, A new compressive video sensing framework for mobile broadcast. IEEE Trans. Broadcast. 59(1), 197–205 (2013)

    Article  Google Scholar 

  13. A.N. Netravali, B.G. Haskell, Digital Pictures: Representation, Compression, and Standards (Plenum Press, New York, 1995)

    Book  Google Scholar 

  14. G.A.F. Seber, Multivariate Observations. Wiley Online Library (Wiley, New York, 1984)

    Book  MATH  Google Scholar 

  15. H. Spath, The Cluster Dissection and Analysis Theory FORTRAN Programs Examples (Prentice-Hall, Reading, 1985)

    Google Scholar 

  16. M. Trocan, T. Maugey, J.E. Fowler, B. Pesquet-Popescu, Disparity-compensated compressed-sensing reconstruction for multiview images, in IEEE International Conference on Multimedia and Expo (ICME) (2010), pp. 1225–1229

    Google Scholar 

  17. J.A. Tropp, A.C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)

    Article  MathSciNet  Google Scholar 

  18. J. Watkinson, The MPEG Handbook: MPEG-1, MPEG-2, MPEG-4 (Focal Press, Boston, 2004)

    Google Scholar 

  19. T. Wiegand, G.J. Sullivan, G. Bjontegaard, Overview of the H.264/AVC video coding standard. IEEE Trans. Circuits Syst. Video Technol. 13(7), 560–576 (2003)

    Article  Google Scholar 

  20. X. Wu, W. Dong, X. Zhang, G. Shi, Model-assisted adaptive recovery of compressed sensing with imaging applications. IEEE Trans. Image Process. 21(2), 451–458 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xi Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi, W., Chen, X. & Li, J. Nonlocally Adaptive Pattern Classification Based Compressed Sensing for Video Recovery. Circuits Syst Signal Process 33, 241–256 (2014). https://doi.org/10.1007/s00034-013-9636-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-013-9636-x

Keywords

Navigation