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2020-09-22
A New Non-Convex Approach for Compressive Sensing MRI
By
Progress In Electromagnetics Research C, Vol. 105, 203-215, 2020
Abstract
Compressive sensing (CS) is an effective method for reconstructing magnetic resonance imaging (MRI) image from under-determined linear system (ULS). However, how to improve the accuracy of MRI image reconstructed by CS is still a serious problem, especially in noisy conditions. To solve this problem, in this paper, we propose a novel approach, dubbed as regularized maximum entropy function (RMEF) minimization algorithm. Specifically, motivated by the entropy function in information theory, we propose a maximum entropy function (MEF) to approximate Lq-norm (0 < q < 1) as sparsity promoting objectives, and then the regularization mechanism for improving the de-noising performance is adopted. Combining the above two ideas, a new objective function of RMEF method is proposed, and the global minimum is iteratively solved. We further analyze the convergence to verify the robustness of the RMEF algorithm. Experiments demonstrate the state-of-the-art performances of the proposed RMEF algorithm and show that the RMEF achieves higher PSNR and SSIM than other widely-adopted methods in MRI image recovery.
Citation
Huihui Yue, and Xiangjun Yin, "A New Non-Convex Approach for Compressive Sensing MRI," Progress In Electromagnetics Research C, Vol. 105, 203-215, 2020.
doi:10.2528/PIERC20051505
References

1. Donoho, D. L., "Compressed sensing," IEEE Transactions on Information Theory, Vol. 4, 1289-1306, 2006.

2. Baraniuk, R. G., E. Candes, R. Nowak, and M. Vetterli, "Compressive sampling," IEEE Signal Processing Magazine, Vol. 25, 12-13, 2008.

3. Candés, E. J. and M. B.Wakin, "An introduction to compressive sampling," IEEE Signal Processing Magazine, Vol. 2, 21-30, 2008.

4. Huang, S. and T. D. Tran, "Sparse signal recovery via generalized entropy functions minimization," Eprint Arxiv, 2017.

5. Candés, E. J., "The restricted isometry property and its implications for compressed sensing," Comptes rendus-Math´ematique, Vol. 346, 589-592, 2008.

6. Natarajan, B. K., "Sparse approximate solutions to linear systems," SIAM Journal on Computing, Vol. 2, 227-234, 1995.

7. Wang, J., S. Kwon, P. Li, and B. Shim, "Recovery of sparse signals via generalized orthogonal matching pursuit: A new analysis," IEEE Transactions on Signal Processing, Vol. 64, 1076-1089, 2016.

8. Lee, J., G. T. Gil, and H. L. Yong, "Channel estimation via orthogonal matching pursuit for hybrid mimo systems in millimeter wave communications," IEEE Transactions on Communications, Vol. 64, 2370-2386, 2016.

9. Wen, J., Z. Zhou, J. Wang, X. Tang, and Q. Mo, "A sharp condition for exact support recovery with orthogonal matching pursuit," IEEE Transactions on Signal Processing, Vol. 6, 1370-1382, 2017.

10. Liu, J., C. Zhang, and C. Pan, "Priori-information hold subspace pursuit: A compressive sensing-based channel estimation for layer modulated TDS-OFDM," IEEE Trans. Broadcast., Vol. 99, 1-9, 2018.

11. Foucart, S. and M. J. Lai, "Sparsest solutions of underdetermined linear systems via Lp-minimization for 0 < p ≤ 1," Applied and Computational Harmonic Analysis, Vol. 3, 395-407, 2009.

12. Hurley, N. and S. Rickard, "Comparing measures of sparsity," IEEE Transactions on Information Theory, Vol. 10, 4723-4741, 2009.

13. Kose, K., O. Gunay, and A. E. Ceti, "Compressive sensing using the modified entropy functional," Digital Signal Processing, Vol. 24, 63-70, 2014.

14. Figueiredo, M. A. T., R. D. Nowak, and S. J.Wright, "Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems," IEEE Journal of Selected Topics in Signal Processing, Vol. 1, 586-597, 2008.

15. Qiao, B., X. Zhang, C.Wang, H. Zhang, and X. Chen, "Sparse regularization for force identification using dictionaries," J. Sound Vib., Vol. 368, 71-86, 2016.

16. Wang, Y., S. Xie, and Z. Xie, "Fista-based papr reduction method for tone reservation’s OFDM system," IEEE Wireless Communications Letters, Vol. 7, No. 3, 300-303, 2017.

17. Metzler, C. A., A. Maleki, and R. G. Baraniuk, "From denoising to compressed sensing," IEEE Transactions on Information Theory, Vol. 62, 5117-5144, 2016.

18. Metzler, C. A., A. Mousavi, and R. G. Baraniuk, "Learned D-AMP: Principled neural network based compressive image recovery," Advances in Neural Information Processing Systems, 2017.

19. Chen, L. and Y. Gu, "On the null space constant for Lp minimization," IEEE Signal Processing Letters, Vol. 10, 1600-1603, 2015.

20. Wang, J. and B. Shim, "A simple proof of the mutual incoherence condition for orthogonal matching pursuit," Mathematics, 2011.

21. Barnett, A. G., J. Beyersmann, and A. Allignol, "The time-dependent bias and its effect on extra length of stay due to nosocomial infection," Value in Health, Vol. 2, 381-386, 2011.

22. Bolyog, B. and G. Pap, "On conditional least squares estimation for affine diffusions based on continuous time observations," Statistical Inference for Stochastic Processes, Vol. 4, 1-35, 2017.

23. Abgrall, R., D. Amsallem, and R. Crisonovan, "Robust model reduction of hyperbolic problems by L1-norm minimization and dictionary approximation," Advanced Modeling and Simulation in Engineering Sciences, Vol. 1, 1, 2016.

24. Zhao, Y., Z. Liu, and Y. Wang, "Sparse coding algorithm with negentropy and weighted L1-norm for signal reconstruction," Entropy, Vol. 1, 599, 2017.

25. Zheng, L., A. Maleki, H. Weng, X. Wang, and T. Long, "Does lp-minimization outperform l1-minimization," IEEE Transactions on Information Theory, Vol. 63, 6896-6935, 2017.

26. Saab, R, R. Chartrand, and O. Yilmaz, "Stable sparse approximations via nonconvex optimization," Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 3885-3888, 2008.

27. Pant, J. K., W. Lu, and A. Antoniou, "Unconstrained regularized Lp norm based algorithm for the reconstruction of sparse signals," IEEE International Symposium on Circuits & Systems, 1740-1743, 2011.

28. Pant, J. K., W. Lu, and A. Antoniou, "New improved algorithms for compressive sensing based on Lp-norm," IEEE Trans. Circuits and Systems II: Express Briefs, Vol. 3, 198-202, 2014.

29. Boyd, S., N. Parikh, E. Chu, B. Peleato, and J. Eckstein, "Distributed optimization and statistical learning via the alternating direction method of multipliers," Found. Trends Mach. Learn., Vol. 1, 1-122, 2011.

30. Xie, Q., C. Ma, and C. Guo, "Image fusion based on the △1-TV energy function," Entropy, Vol. 16, 6099-6115, 2014.

31. Du, S. and M. Chen, "A new smoothing modified three-term conjugate gradient method for L1-norm minimization problem," Journal of Inequalities and Applications, Vol. 1, 105, 2018.

32. Lai, M. J., Y. Xu, and W. Yin, "Improved iteratively reweighted least squares for unconstrained smoothed Lq minimization," SIAM Journal on Numerical Analysis, Vol. 51, 927-957, 201.

33. Li, Q., S. Y. Liang, and Q. Li, "Incipient fault diagnosis of rolling bearings based on impulse-step impact dictionary and re-weighted minimizing nonconvex penalty Lq regular technique," Entropy, Vol. 19, 2017.

34. Wipf, D. and S. Nagarajan, "Iterative reweighted L1 and L2 methods for finding sparse solutions," IEEE Journal of Selected Topics in Signal Processing, Vol. 4, 317-329, 2013.

35. Ye, X., W. Zhu, and A. Zhang, "Sparse channel estimation of MIMO-OFDM systems with unconstrained smoothed L0-norm-regularized least squares compressed sensing," EURASIP Journal on Wireless Communications and Networking, Vol. 1, 282, 2013.

36. Arias-Castro, E. and Y. C. Eldar, "Noise folding in compressed sensing," IEEE Signal Processing Letters, Vol. 18, 478-481, 2011.

37. Yang, X., Q. Cui, E. Dutkiewicz, and X. Huang, "Anti-noise-folding regularized subspace pursuit recovery algorithm for noisy sparse signals," Proceeding of the IEEE Wireless Communications and Networking Conference, 275-280, Istanbul, Turkey, April 6-9, 2014.

38. Lu, Z., "Iterative reweighted minimization methods for lp regularized unconstrained nonlinear programming," Mathematical Programming, Vol. 147, 277-307, 2014.

39. Mourad, N., J. P. Reilly, and T. Kirubarajan, "Majorization-minimization for blind source separation of sparse sources," Signal Processing, Vol. 131, 120-133, 2017.

40. Oh, J. and N. Kwak, "Generalized mean for robust principal component analysis," Pattern Recognition, Vol. 54, 116-127, 2016.

41. Zhou, W., Y. B. Sun, Q. S. Liu, and W. U. Min, "L0 group sparse RPCA model and algorithm for moving object detection," Acta Electronica Sinica, Vol. 44, No. 3, 627-632, 2016.

42. Xu, D., X. Gao, X. Fan, D. Zhao, and W. Gao, "ODD: An algorithm of online directional dictionary learning for sparse representation," Proceedings of the Pacific Rim Conference on Multimedia, Vol. 10736, 939-947, Harbin, China, September 28-29, 2017.