Sparse reconstruction of magnetic resonance image combined with two-step iteration and adaptive shrinkage factor

Xiuhan Li; Rui Feng; Funan Xiao; Yue Yin; Da Cao; Xiaoling Wu; Songsheng Zhu; Wei Wang; Xiuhan Li; Rui Feng; Funan Xiao; Yue Yin; Da Cao; Xiaoling Wu; Songsheng Zhu; Wei Wang

doi:10.3934/mbe.2022618

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 13214-13226. doi: 10.3934/mbe.2022618

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Sparse reconstruction of magnetic resonance image combined with two-step iteration and adaptive shrinkage factor

1.
Key Laboratory of Clinical Engineering, School of Biomedical Engineering and Informatics, Nanjing Medical University, Nanjing 211166, China
2.
Jiangsu Province Hospital of Chinese Medicine, Affiliated Hospital of Nanjing University of Chinese Medicine, Nanjing 210029, China
3.
Department of Medical Engineering, Jiangbei Branch of Zhongda Hospital Affiliated to Southeast University, Nanjing 210044, China
4.
Department of Radiology, The First Affiliated Hospital of Nanjing Medical University, Nanjing, 210029, China

Academic Editor: Simon James Fong
^† The authors contributed equally to this work.

Received: 20 July 2022 Revised: 02 September 2022 Accepted: 05 September 2022 Published: 09 September 2022

As an advanced technique, compressed sensing has been used for rapid magnetic resonance imaging in recent years, Two-step Iterative Shrinkage Thresholding Algorithm (TwIST) is a popular algorithm based on Iterative Thresholding Shrinkage Algorithm (ISTA) for fast MR image reconstruction. However TwIST algorithms cannot dynamically adjust shrinkage factor according to the degree of convergence. So it is difficult to balance speed and efficiency. In this paper, we proposed an algorithm which can dynamically adjust the shrinkage factor to rebalance the fidelity item and regular item during TwIST iterative process. The shrinkage factor adjusting is judged by the previous reconstructed results throughout the iteration cycle. It can greatly accelerate the iterative convergence while ensuring convergence accuracy. We used MR images with 2 body parts and different sampling rates to simulate, the results proved that the proposed algorithm have a faster convergence rate and better reconstruction performance. We also used 60 MR images of different body parts for further simulation, and the results proved the universal superiority of the proposed algorithm.
- compressed sensing,
- MR imaging reconstruction,
- iterative shrinkage thresholding,
- two-step iterative,
- dynamic shrinkage factor
Citation: Xiuhan Li, Rui Feng, Funan Xiao, Yue Yin, Da Cao, Xiaoling Wu, Songsheng Zhu, Wei Wang. Sparse reconstruction of magnetic resonance image combined with two-step iteration and adaptive shrinkage factor[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 13214-13226. doi: 10.3934/mbe.2022618

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Abstract

As an advanced technique, compressed sensing has been used for rapid magnetic resonance imaging in recent years, Two-step Iterative Shrinkage Thresholding Algorithm (TwIST) is a popular algorithm based on Iterative Thresholding Shrinkage Algorithm (ISTA) for fast MR image reconstruction. However TwIST algorithms cannot dynamically adjust shrinkage factor according to the degree of convergence. So it is difficult to balance speed and efficiency. In this paper, we proposed an algorithm which can dynamically adjust the shrinkage factor to rebalance the fidelity item and regular item during TwIST iterative process. The shrinkage factor adjusting is judged by the previous reconstructed results throughout the iteration cycle. It can greatly accelerate the iterative convergence while ensuring convergence accuracy. We used MR images with 2 body parts and different sampling rates to simulate, the results proved that the proposed algorithm have a faster convergence rate and better reconstruction performance. We also used 60 MR images of different body parts for further simulation, and the results proved the universal superiority of the proposed algorithm.

References

[1]	D. Donoho, Compressed sensing, IEEE Trans. Inf. Theory, 52 (2006), 1289–1306. https://doi.org/10.1109/TIT.2006.871582 doi: 10.1109/TIT.2006.871582
[2]	M. Lustig, D. Donoho, J. M. Pauly, Sparse MRI: The application of compressed sensing for rapid MR imaging, Magn. Reson. Med., 58 (2007), 1182–1195. https://doi.org/10.1002/mrm.21391 doi: 10.1002/mrm.21391
[3]	I. Daubechies, M. Defrise, C. D. Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Commun. Pure Appl. Math., 57 (2004), 1413–1457. https://doi.org/10.1002/cpa.20042 doi: 10.1002/cpa.20042
[4]	T. Goldstein, S. Osher, The Split Bregman method for L1-egularized problems, SIAM J. Imaging Sci., 2 (2009), 1–21. https://doi.org/10.1137/080725891 doi: 10.1137/080725891
[5]	W. W. Hager, H. Zhang, A survey of nonlinear conjugate gradient methods, Pac. J. Optim., 2 (2006), 35–58. https://doi.org/10.1006/jsco.1995.1040 doi: 10.1006/jsco.1995.1040
[6]	H. Nien, J. A. Fessler, A convergence proof of the split Bregman method for regularized least-squares problems, Mathematics, 2014 (2014). https://doi.org/10.48550/arXiv.1402.4371 doi: 10.48550/arXiv.1402.4371
[7]	J. D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyré, Iterative Bregman projections for regularized transportation problems, SIAM J. Sci. Comput., 37 (2015). https://doi.org/10.1137/141000439 doi: 10.1137/141000439
[8]	E. G. Birgin, J. M. Martínez, A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim., 43 (2001), 117–128. https://doi.org/10.1007/s00245-001-0003-0 doi: 10.1007/s00245-001-0003-0
[9]	M. M. Dehnavi, D. M. Fernandez, D. Giannacopoulos, Enhancing the performance of conjugate gradient solvers on graphic processing units, IEEE Trans. Magn., 47 (2011), 1162–1165. https://doi.org/10.1109/TMAG.2010.2081662 doi: 10.1109/TMAG.2010.2081662
[10]	S. Wang, Z. Su, L. Ying, X. Peng, S. Zhu, F. Liang, et al., Accelerating magnetic resonance imaging via deep learning, in 2016 IEEE 13th International Symposium on Biomedical Imaging (ISBI), (2016), 514–517. https://doi.org/10.1109/ISBI.2016.7493320
[11]	D. Liang, J. Cheng, Z. Ke, L. Ying, Deep magnetic resonance image reconstruction: Inverse problems meet neural networks, IEEE Signal Process. Mag., 37 (2020), 141–151. https://doi.org/10.1109/MSP.2019.2950557 doi: 10.1109/MSP.2019.2950557
[12]	J. M. Bioucas-Dias, M. A. T. Figueiredo, A new twIst: Two-step iterative shrinkage/thresholding algorithms for image restoration, IEEE Trans. Image Process., 16 (2007), 2992–3004. https://doi.org/10.1109/tip.2007.909319 doi: 10.1109/tip.2007.909319
[13]	A. Beck, M. Teboulle, A fast Iterative Shrinkage-Thresholding Algorithm with application to wavelet-based image deblurring, in 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, (2009), 693–696. https://doi.org/10.1109/ICASSP.2009.4959678
[14]	Y. Zhang, Z. Dong, P. Phillips, S. Wang, G. Ji, J. Yang, Exponential Wavelet Iterative Shrinkage Thresholding Algorithm for compressed sensing magnetic resonance imaging, Inf. Sci., 322 (2015), 115–132. https://doi.org/10.1016/j.ins.2015.06.017 doi: 10.1016/j.ins.2015.06.017
[15]	X. Li, J. Wang, S. Tan, Hessian Schatten-norm regularization for CBCT image reconstruction using fast iterative shrinkage-thresholding algorithm, in Medical Imaging 2015: Physics of Medical Imaging, 2015. https://doi.org/10.1117/12.2082424
[16]	G. Wu, S. Luo, Adaptive fixed-point iterative shrinkage/thresholding algorithm for MR imaging reconstruction using compressed sensing, Magn. Reson. Imaging, 32 (2014), 372–378. https://doi.org/10.1016/j.mri.2013.12.009 doi: 10.1016/j.mri.2013.12.009
[17]	K. Shang, Y. Li, Z. Huang, Iterative p-shrinkage thresholding algorithm for low Tucker rank tensor recovery, Inf. Sci., 482 (2019), 374–391. https://doi.org/10.1016/j.ins.2019.01.031 doi: 10.1016/j.ins.2019.01.031
[18]	L. Zhang, H. Wang, Y. Xu, A shrinkage-thresholding method for the inverse problem of Electrical Resistance Tomography, in 2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings, (2012), 2425–2429. https://doi.org/10.1109/I2MTC.2012.6229564
[19]	A. Beck, M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2 (2009), 183–202. https://doi.org/10.1137/080716542 doi: 10.1137/080716542
[20]	A. Chambolle, C. Dossal, On the Convergence of the Iterates of the "Fast Iterative Shrinkage/Thresholding Algorithm", J. Optim. Theory Appl., 166 (2015), 1–15. https://doi.org/10.1007/s10957-015-0746-4 doi: 10.1007/s10957-015-0746-4
[21]	İ. Bayram, On the convergence of the iterative shrinkage/thresholding algorithm with a weakly convex penalty, IEEE Trans. Signal Process., 64 (2016), 1597–1608. https://doi.org/10.1109/TSP.2015.2502551 doi: 10.1109/TSP.2015.2502551
[22]	W. Hao, J. Li, X. Qu, Z. Dong, Fast iterative contourlet thresholding for compressed sensing MRI, Electron. Lett., 49 (2013), 1206. https://doi.org/10.1049/el.2013.1483 doi: 10.1049/el.2013.1483
[23]	S. Dirksen, G. Lecue, H. Rauhut, On the gap between restricted isometry properties and sparse recovery conditions, IEEE Trans. Inf. Theory, 64 (2018), 5478–5487. https://doi.org/10.1109/TIT.2016.2570244 doi: 10.1109/TIT.2016.2570244
[24]	Y. Yang, C. M. Kramer, P. W. Shaw, C. H. Meyer, M. Salerno, First-pass myocardial perfusion imaging with whole-heart coverage using L1-SPIRiT accelerated variable density spiral trajectories, Magn. Reson. Med., 76 (2016), 1375–1387. https://doi.org/10.1002/mrm.26014 doi: 10.1002/mrm.26014
[25]	V. P. Gopi, P. Palanisamy, K. A. Wahid, P. Babyn, D. Cooper, Multiple regularization based MRI reconstruction, Signal Process., 103 (2014), 103–113. https://doi.org/10.1016/j.sigpro.2013.11.001 doi: 10.1016/j.sigpro.2013.11.001
[26]	C. S. Xydeas, V. S. Petrovic, Objective image fusion performance measure, Electron. Lett., 36 (2000), 308–309. https://doi.org/10.1117/12.381668 doi: 10.1117/12.381668

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