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Multi-Resolution Kronecker Compressive Sensing

  • Canh, Thuong Nguyen (Department of Electronic and Electrical Engineering, Sungkyunkwan University) ;
  • Quoc, Khanh Dinh (Department of Electronic and Electrical Engineering, Sungkyunkwan University) ;
  • Jeon, Byeungwoo (Department of Electronic and Electrical Engineering, Sungkyunkwan University)
  • Received : 2013.10.20
  • Accepted : 2013.11.15
  • Published : 2014.02.28

Abstract

Compressive sensing is an emerging sampling technique which enables sampling a signal at a much lower rate than the Nyquist rate. In this paper, we propose a novel framework based on Kronecker compressive sensing that provides multi-resolution image reconstruction capability. By exploiting the relationship of the sensing matrices between low and high resolution images, the proposed method can reconstruct both high and low resolution images from a single measurement vector. Furthermore, post-processing using BM3D improves its recovery performance. The experimental results showed that the proposed scheme provides significant gains over the conventional framework with respect to the objective and subjective qualities.

Keywords

References

  1. D. Donoho, "Compressed sensing," IEEE Trans. Info. Theory, vol. 52, no. 4, pp. 1289-1306, 2006. Article (CrossRef Link) https://doi.org/10.1109/TIT.2006.871582
  2. S. Mun and E. Fowler, "Block compressed sensing of images using directional transforms," in Proc. IEEE Intern. Conf. on Image Process.(ICIP), pp. 3021-3024, USA, 2009. Article (CrossRef Link)
  3. K. Q. Dinh, H. J. Shim, and B. Jeon, "Measurement coding for compressive Imaging based on structured measuremnet matrix," in Proc. IEEE Intern. Conf. on Image Process.(ICIP), pp. 10-13, 2013. Article (CrossRef Link)
  4. M. Duarte and R. Baraniuk, "Kronecker compressive sensing," IEEE Trans. Image Process., vol.21, no.2, pp. 494-504, 2012. Article (CrossRef Link) https://doi.org/10.1109/TIP.2011.2165289
  5. T. Goldstein and S. Osher, "The split Bregman method for L1 regularized problems," SIAM J. on Imaging Sci., vol. 2, no. 2, pp. 323-343, 2009. Article (CrossRef Link) https://doi.org/10.1137/080725891
  6. S. Shishkin, H.Wang, and G. Hagen, "Total variation minimization with separable sensing operator," in Proc. Conf. on Image and Signal Process.(ICISP), pp. 86-93, 2010. Article (CrossRef Link)
  7. T. N. Canh, K. Q. Dinh and B. Jeon, "Total variation for Kronecker compressive sensing with new regularization," in Proc. Pic. Coding Symp.(PCS), pp. 261-264. 2013. Article (CrossRef Link)
  8. A. K. Katsagellos, R. Mollina, and J. Mateos, Super-Resolution of Images and Video, Morgan & Claypool, 2007. Article (CrossRef Link)
  9. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, "Image denoising by sparse 3D transform-domain collaborative filtering," IEEE Trans. Image Process., vol. 16, no. 8, pp. 2080-2095, 2007. Article (CrossRef Link) https://doi.org/10.1109/TIP.2007.901238
  10. Y. Kim, H. Oh, and A. Bilgin, "Video compressed sensing using iterative self-similarity modeling and residual reconstruction," J. of Electron. Imaging, vol. 22. no.2, pp. 021005, 2013. Article (CrossRef Link) https://doi.org/10.1117/1.JEI.22.2.021005
  11. D. Valseia and E. Magli, "Spatially scalable compressed image sensing with hybrid transform and inter-layer prediction model," in IEEE Inter. Workshop on Multimedia Signal Process.(MMSP), pp. 373-378, 2013. Article (CrossRef Link)
  12. A. Sankaranarayanan, C. Studer, and R. Baraniuk, "CS-MUVI: Video compressive sensing for spatialmultiplexing cameras," in IEEE Inter. Conf. Computational Photography (ICCP), pp. 1-10, Apr. 2012. Article (CrossRef Link)
  13. T. Goldstein, L. Xu, K. F. Kelly, and R. G. Baraniuk, "The STONE transform: multi-resolution image enhancement and real-time compressive video," Available at Arxiv.org (arXiv:1311.3405), 2013. Article (CrossRef Link)
  14. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, "Single-pixel imaging via compressive sampling," IEEE Signal Process. Mag., vol. 25, pp. 83-91, 2008. Article (CrossRef Link) https://doi.org/10.1109/MSP.2007.914730
  15. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, "Image quality assessment: From error measurement to structural similarity," IEEE Trans. Image Process., vol. 13, no. 4, pp. 600-612, 2004. Article (CrossRef Link) https://doi.org/10.1109/TIP.2003.819861
  16. R. G. Keys, "Cubic Convolution Interpolation for Digital Image Proceeding," IEEE Transactions on Acoustics, Speech, Signal Process., vol. 29, no. 6, pp. 1153-1160, 1981. Article (CrossRef Link) https://doi.org/10.1109/TASSP.1981.1163711
  17. J. Y. Park and M. B. Wakin, "A multiscale framework for compressive sensing of video," in Proc. of Pict. Coding Symp.(PCS), pp. 1-4, 2009. Article (CrossRef Link)
  18. C. Li, W. Yin and Y. Zhang, "An efficient augmented Lagragian method with applications to total variation minimization," in Comput. Optimization and Application, vol. 56, not. 3, pp. 507-530, 2013. Article (CrossRef Link) https://doi.org/10.1007/s10589-013-9576-1