Blind compressed sensing using sparsifying transforms

2015 International Conference on Sampling Theory and Applications, SampTA 2015

Volumn , Issue , 2015, Pages 513-517

  Ravishankar, Saiprasad ^a   Bresler, Yoram ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSED SENSING; MAGNETIC RESONANCE IMAGING;

A-TRANSFORM; BLOCK COORDINATE DESCENTS; IMAGE PATCHES; K SPACE; NONCONVEX; UNDER-SAMPLED;

IMAGE RECONSTRUCTION;

EID: 84941031235     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SAMPTA.2015.7148944     Document Type: Conference Paper

References (19)

1. D. Donoho, "Compressed sensing," IEEE Trans. Information Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
2. M. Lustig, D. Donoho, and J. Pauly, "Sparse MRI: The application of compressed sensing for rapid MR imaging," Magnetic Resonance in Medicine, vol. 58, no. 6, pp. 1182-1195, 2007.
3. S. Ravishankar and Y. Bresler, "MR image reconstruction from highly undersampled k-space data by dictionary learning," IEEE Trans. Med. Imag., vol. 30, no. 5, pp. 1028-1041, 2011.
4. S. Gleichman and Y. C. Eldar, "Blind compressed sensing," IEEE Trans. Inf. Theory, vol. 57, no. 10, pp. 6958-6975, 2011.
5. S. G. Lingala and M. Jacob, "Blind compressive sensing dynamic mri," IEEE Trans. Med. Imag., vol. 32, no. 6, pp. 1132-1145, 2013.
6. S. Ravishankar and Y. Bresler, "Learning sparsifying transforms," IEEE Trans. Signal Process., vol. 61, no. 5, pp. 1072-1086, 2013.
7. -, "Efficient blind compressed sensing using sparsifying transforms with convergence guarantees and application to MRI," 2015, preprint: http://arxiv.org/abs/1501.02923.
8. -, "0 sparsifying transform learning with efficient optimal updates and convergence guarantees," IEEE Trans. Signal Process., vol. 63, no. 9, pp. 2389-2404, May 2015.
9. G. H. Golub and C. F. V. Loan, Matrix Computations. Johns Hopkins University Press, 1996.
10. M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation," IEEE Transactions on signal processing, vol. 54, no. 11, pp. 4311-4322, 2006.
11. P. Tseng, "Convergence of a block coordinate descent method for nondifferentiable minimization," J. Optim. Theory Appl., vol. 109, no. 3, pp. 475-494, 2001.
12. E. Chouzenoux, J.-C. Pesquet, and A. Repetti, "A block coordinate variable metric forward-backward algorithm," 2014, preprint: http:// www.optimization-online.org/DB HTML/2013/12/4178.html.
13. R. T. Rockafellar and R. J.-B. Wets, Variational Analysis, 1st edn. Springer-Verlag, 1997.
14. B. Ning, X. Qu, D. Guo, C. Hu, and Z. Chen, "Magnetic resonance image reconstruction using trained geometric directions in 2d redundant wavelets domain and non-convex optimization," Magnetic Resonance Imaging, vol. 31, no. 9, pp. 1611-1622, 2013.
15. M. Lustig, "Michael Lustig home page," http://www.eecs.berkeley.edu/ ~mlustig/Software.html, 2014, [Online; accessed October, 2014].
16. X. Qu, "PBDWS Code," http://www.quxiaobo.org/project/CS MRI PBDWS/Demo PBDWS SparseMRI.zip, 2014, [Online; accessed September, 2014].
17. S. Ravishankar and Y. Bresler, "DLMRI-Lab: Dictionary learning MRI software," http://www.ifp.illinois.edu/~yoram/DLMRI-Lab/ DLMRI.html, 2013, [Online; accessed October, 2014].
18. B. Wen, S. Ravishankar, and Y. Bresler, "Structured overcomplete sparsifying transform learning with convergence guarantees and applications," International Journal of Computer Vision, pp. 1-31, 2014.
19. X. Qu, Y. Hou, F. Lam, D. Guo, J. Zhong, and Z. Chen, "Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator," Medical Image Analysis, vol. 18, no. 6, pp. 843-856, 2014.