volume | PIER Journals

Abstract

In this paper, the main problem to be solved is how to achieve magnetic resonance imaging (MRI) accurately and quickly. Previous work has shown that compressive sensing (CS) technology can reconstruct a magnetic resonance (MR) image from only a small number of samples, which significantly reduces MR scanning time. Based on this, an algorithm to improve the accuracy of MRI, called regularized weighting Composite Gaussian smoothed l₀-norm minimization (RWCGSL0), is proposed in this paper. Different from previous methods, our algorithm has three influential contributions: (1) a new smoothed Composite Gaussian function (CGF) is proposed to be closer to the l₀-norm; (2) a new weighting function is proposed; (3) a new l₀ regularized objective function framework is constructed. Furthermore, the optimal solution of this objective function is obtained by penalty decomposition (PD)method. It is experimentally shown that the proposed algorithm outperforms other state-of-the-art CS algorithms in the reconstruction of MR images.

1. Shrividya, G. and S. H. Bharathi, "Application of compressed sensing on magnetic resonance imaging: A brief survey," IEEE International Conference on Recent Trends in Electronics, Information & Communication Technology, 2037-2041, 2017.

2. Donoho, D. L., "Compressed sensing," IEEE Transactions on Information Theory, Vol. 52, No. 4, 1289-1306, 2006.
doi:10.1109/TIT.2006.871582

3. Badenska, A. and L. Blaszczyk, "Compressed sensing for real measurements of quaternion signals," Journal of the Franklin Institute, Vol. 354, No. 13, 5753-5769, 2017.
doi:10.1016/j.jfranklin.2017.06.004

4. Candes, E. J. and M. B. Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, Vol. 25, No. 2, 21-30, 2008.
doi:10.1109/MSP.2007.914731

5. Lang, C., H. Li, G. Li, and X. Zhao, "Combined sparse representation based on curvelet transform and local DCT for multi-layered image compression," IEEE International Conference on Communication Software and Networks, Vol. 220, No. 6, 316-320, 2011.

6. Candes, E. J., J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Transactions on Information Theory, Vol. 52, No. 2, 489-509, 2006.
doi:10.1109/TIT.2005.862083

7. Tropp, J. A. and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," IEEE Transactions on Information Theory, Vol. 53, No. 12, 4655-4666, 2007.
doi:10.1109/TIT.2007.909108

8. Jian, W., K. Seokbeop, and S. Byonghyo, "Generalized orthogonal matching pursuit," IEEE Transactions on Signal Processing, Vol. 60, No. 12, 6202-6216, 2012.
doi:10.1109/TSP.2012.2218810

9. Needell, D. and J. A. Tropp, "CoSaMP: Iterative signal recovery from incomplete and inaccurate samples," Applied & Computational Harmonic Analysis, Vol. 26, No. 3, 301-321, 2009.
doi:10.1016/j.acha.2008.07.002

10. Dai, W. and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," IEEE Transactions on Information Theory, Vol. 55, No. 5, 2230-2249, 2009.
doi:10.1109/TIT.2009.2016006

11. Chen, S. S., D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM Review, Vol. 43, No. 1, 129-159, 2001.
doi:10.1137/S003614450037906X

12. Zhai, Y., J. Gan, Y. Xu, and J. Zeng, "Fast sparse representation for Finger-Knuckle-Print recognition based on smooth L0 norm," IEEE International Conference on Signal Processing, 1587-1591, 2013.

13. Xiao, J., C. R. Del-Blanco, C. Cuevas, and N. Garcıa, "Fast image decoding for block compressed sensing based encoding by using a modified smooth l0-norm," IEEE International Conference on Consumer Electronics, 234-236, 2016.

14. Wang, H., Q. Guo, G. Zhang, G. Li, and W. Xiang, "Thresholded smoothed 0 norm for accelerated sparse recovery," IEEE Communications Letters, Vol. 19, No. 6, 953-956, 2015.
doi:10.1109/LCOMM.2015.2416711

15. Ghalehjegh, S. H., M. Babaie-Zadeh, and C. Jutten, "Fast block-sparse decomposition based on SL0," International Conference on Latent Variable Analysis and Signal Separation, 426-433, 2010.
doi:10.1007/978-3-642-15995-4_53

16. Zhao, R., W. Lin, L. Hao, and A. H. Shaohai, "Reconstruction algorithm for compressive sensing based on smoothed l0 norm and revised newton method," Journal of Computer-Aided Design & Computer Graphics, Vol. 24, No. 4, 478-484, 2012.

17. Ye, X., W. P. Zhu, A. Zhang, and J. Yan, "Sparse channel estimation of MIMO-OFDM systems with unconstrained smoothed l0-norm-regularized least squares compressed sensing," Eurasip Journal on Wireless Communications & Networking, Vol. 2013, No. 1, 282, 2013.
doi:10.1186/1687-1499-2013-282

18. Ye, X. and W. P. Zhu, "Sparse channel estimation of pulse-shaping multiple-input-multipleoutput orthogonal frequency division multiplexing systems with an approximate gradient l2-l0 reconstruction algorithm," Iet Communications, Vol. 8, No. 7, 1124-1131, 2014.
doi:10.1049/iet-com.2013.0571

19. Soussen, C., J. Idier, J. Duan, and D. Brie, "Homotopy based algorithms for l0-regularized leastsquares," IEEE Transactions on Signal Processing, Vol. 63, No. 13, 3301-3316, 2015.
doi:10.1109/TSP.2015.2421476

20. Yin, W., D. Goldfarb, and S. Osher, "The total variation regularized Lsp1 model for multiscale decomposition," Siam Journal on Multiscale Modeling & Simulation, Vol. 6, No. 1, 190-211, 2013.
doi:10.1137/060663027

21. Pant, J. K., W. S. Lu, and A. Antoniou, "New improved algorithms for compressive sensing based on p norm," IEEE Transactions on Circuits & Systems II Express Briefs, Vol. 61, No. 3, 198-202, 2014.
doi:10.1109/TCSII.2013.2296133

22. Malek-Mohammadi, M., A. Koochakzadeh, M. Babaie-Zadeh, M. Jansson, and C. R. Rojas, "Successive concave sparsity approximation for compressed sensing," IEEE Transactions on Signal Processing, Vol. 64, No. 21, 5657-5671, 2016.
doi:10.1109/TSP.2016.2585096

23. Li, S., H. Yin, and L. Fang, "Remote sensing image fusion via sparse representations over learned dictionaries," IEEE Transactions on Geoscience & Remote Sensing, Vol. 51, No. 9, 4779-4789, 2013.
doi:10.1109/TGRS.2012.2230332

24. Zhang, J., D. Zhao, F. Jiang, and W. Gao, "Structural group sparse representation for image compressive sensing recovery," IEEE International Conference on Data Compression, 331-340, 2013.

25. Hawes, M. B. and W. Liu, "Robust sparse antenna array design via compressive sensing," International Conference on Digital Signal Processing, 1-5, 2013.

26. Lu, Z. and Y. Zhang, "Penalty decomposition methods for L0-norm minimization," Mathematics, 2010.

27. Shi, Z., "A weighted block dictionary learning algorithm for classification," Mathematical Problems in Engineering, Vol. 2016, 2016.

28. Candes, E. J., M. B. Wakin, and S. P. Boyd, "Enhancing sparsity by reweighted L1 minimization," Journal of Fourier Analysis & Applications, Vol. 14, No. 5–6, 877-905, 2008.
doi:10.1007/s00041-008-9045-x

29. Rudin, L. I., S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D Nonlinear Phenomena, Vol. 60, No. 1-4, 259-268, 1992.
doi:10.1016/0167-2789(92)90242-F

30. Wen, F., Y. Yang, P. Liu, R. Ying, and Y. Liu, "Efficient q minimization algorithms for compressive sensing based on proximity operator," Mathematics, 2016.

Dr. Huihui Yue

Dr. Xiangjun Yin