Proximal smoothing iterative algorithm for magnetic resonance image reconstruction based on Moreau-envelope

doi:10.11772/j.issn.1001-9081.2017122980

Journal of Computer Applications ›› 2018, Vol. 38 ›› Issue (7): 2076-2082.DOI: 10.11772/j.issn.1001-9081.2017122980

Previous Articles Next Articles

Proximal smoothing iterative algorithm for magnetic resonance image reconstruction based on Moreau-envelope

LIU Xiaohui, LU Lijun, FENG Qianjin, CHEN Wufan

School of Biomedical Engineering, Southern Medical University, Guangzhou Guangdong 510515, China

Received:2017-12-20 Revised:2018-01-31 Online:2018-07-10 Published:2018-07-12
Supported by:
This work is partially supported by the National Key Research and Development Program (2016YFC0104003), the National Natural Science Foundation of China (81501541).

基于Moreau-包络的近似平滑迭代磁共振图像重建算法

刘晓晖, 路利军, 冯前进, 陈武凡

南方医科大学生物医学工程学院, 广州 510515

通讯作者: 陈武凡
作者简介:刘晓晖(1986-),女,江苏宿迁人,博士研究生,主要研究方向:医学图像重建、优化算法;路利军(1984-),男,山西岢岚人,副教授,博士,主要研究方向:医学图像重建、正电子发射型计算机断层显像成像分析;冯前进(1974-),男,河南武修人,教授,博士,主要研究方向:医学图像分析、医学成像方法;陈武凡(1949-),男,湖南汨罗人,教授,硕士,主要研究方向:医学图像处理、模式识别、神经网络。
基金资助:
国家重点研发专项（2016YFC0104003）；国家自然科学基金资助项目（81501541）。

Abstract

Abstract: To solve the problem of two non-smooth regularization terms in sparse reconstruction of Magnetic Resonance Imaging (MRI) based on Compressed Sensing (CS), a new Proximal Smoothing Iterative Algorithm (PSIA) based on Moreau-envelope was proposed. The classical sparse reconstruction for MRI based on CS is a problem of minimizing the objective function with a linear combination of three terms:the least square data fidelity term, the sparse regularization term of wavelet transform, and the Total Variation (TV) regularization term. Firstly, the proximal smoothing of the wavelet transform regularization term in the objective function was carried out. Then, the linear combination of the data fidelity term and the wavelet transform regularization term after smooth approximation was considered as a new convex function that could be continuously derived. Finally, PSIA was used to solve the new optimization problem. The proposed algorithm can not only cope with the two regularization constraints simultaneously in the optimization problem, but also avoid the algorithm robustness problem caused by fixed weights. The experimental results on simulated phantom images and real MR images show that, compared with four classical sparse reconstruction algorithms such as Conjugate Gradient (CG) decent algorithm, TV l₁ Compressed MRI (TVCMRI) algorithm, Reconstruction From Partial k space algorithm (RecPF) and Fast Composite Smoothing Algorithm (FCSA), the proposed algorithm has better reconstruction results of image signal-to-noise ratio, relative error and structural similarity index, and its algorithm complexity is comparable to the existing fastest reconstruction algorithm FCSA.

Key words: Compressed Sensing (CS), Magnetic Resonance (MR) image reconstruction, sparse reconstruction, convex optimization, proximal smoothing

摘要： 针对基于压缩感知（CS）的磁共振成像（MRI）稀疏重建中存在的两个非平滑正则项问题，提出了一种基于Moreau包络的近似平滑迭代算法（PSIA）。基于CS的经典MRI稀疏重建是求解一个由最小二乘保真项、小波变换稀疏正则项和总变分（TV）正则项线性组合成的目标函数最小化问题。首先，对目标函数中的小波变换正则项作平滑近似；然后，将数据保真项与平滑近似后的小波正则项的线性组合看成一个新的可以连续求导的凸函数；最后，采用PSIA对新的优化问题进行求解。该算法不仅可以同时处理优化问题中的两个正则约束项，还避免了固定权重带来的算法鲁棒性问题。仿真得到的体模图像及真实磁共振图像的实验结果表明，所提算法与四种经典的稀疏重建算法：共轭梯度（CG）下降算法、TV1范数压缩MRI（TVCMRI）算法、部分k空间重建算法（RecPF）和快速复合分离算法（FCSA）相比，在图像信噪比、相对误差和结构相似性指数上具有更好的重建结果，且在算法复杂度上与现有最快重建算法即FCSA相当。

关键词: 压缩感知, 磁共振图像重建, 稀疏重建, 凸优化, 近似平滑

CLC Number:

LIU Xiaohui, LU Lijun, FENG Qianjin, CHEN Wufan. Proximal smoothing iterative algorithm for magnetic resonance image reconstruction based on Moreau-envelope[J]. Journal of Computer Applications, 2018, 38(7): 2076-2082.

刘晓晖, 路利军, 冯前进, 陈武凡. 基于Moreau-包络的近似平滑迭代磁共振图像重建算法[J]. 计算机应用, 2018, 38(7): 2076-2082.

References

[1] LIANG Z P, LAUTERBUR P C. Principles of Magnetic Resonance Imaging:a Signal Processing Perspective[M]. Wiley:Wiley-IEEE Press, 1999:1-28.
[2] MCROBBIE D W, MOORE E A, GRAVES M J, et al. MRI from Picture to Proton[M]. Cambridge, UK:Cambridge University Press, 2006:1-25.
[3] COHEN M S, WEISSKOFF R M. Ultra-fast imaging[J]. Magnetic Resonance Imaging, 1991, 9(1):1-37.
[4] LUSTIG M, DONOHO D, PAULY J M. Sparse MRI:the application of compressed sensing for rapid MR imaging[J]. Magnetic Resonance in Medicine, 2007, 58(6):1182-1195.
[5] PRUESSMANN K P, WEIGER M, SCHEIDEGGER M B, et al. SENSE:sensitivity encoding for fast MRI[J]. Magnetic Resonance in Medicine, 1999, 42(5):952-962.
[6] SODICCKSON D K, MANNING W J. SiMultaneous Acquisition of Spatial Harmonics (SMASH):fast imaging with radiofrequency coil arrays[J]. Magnetic Resonance in Medicine, 1997, 38(4):591-603.
[7] 王达,包尚联.并行磁共振成像GRAPPA-SENSE技术[J].中国医学影像技术,2011,27(8):1688-1693.(WANG D, BAO S L. Parallel magnetic resonance image technology of GRAPPA-SENSE[J]. Chinese Journal of Medical Imaging Technology, 2011, 27(8):1688-1693.)
[8] 公伟,迟洁茹,杨新强.基于GRAPPA图像重建的采样轨迹[J].计算机应用.2010,30(7):1847-1848.(GONG W, CHI J R, YANG X Q. New trajectory for image reconstruction based on GRAPPA[J]. Journal of Computer Applications, 2010, 30(7):1847-1848.)
[9] CANDES E J, ROMBERG J, TAO T. Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2):489-509.
[10] DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[11] 陈伟业,孙权森.结合压缩感知与非局部信息的图像超分辨率重建[J].计算机应用,2016,36(9):2570-2575.(CHEN W Y, SUN Q S. Image super-resolution reconstruction combined with compressed sensing and nonlocal information[J]. Journal of Computer Applications, 2016, 36(9):2570-2575.)
[12] 杨学峰,程耀瑜,王高.基于小波域压缩感知的遥感图像超分辨算法[J].计算机应用,2017,37(5):1430-1433,1444.(YANG X F, CHENG Y Y, WANG G. Super-resolution algorithm for remote sensing images based on compressive sensing in wavelet domain[J]. Journal of Computer Applications, 2017, 37(5):1430-1433, 1444.)
[13] GABAY D. Chapter IX applications of the method of multipliers to variational inequalities[J]. Studies in Mathematics and its Applications, 1983, 15:299-331.
[14] SPINGARN J E. Partial inverse of a monotone operator[J]. Applied Mathematics and Optimization, 1983, 10(1):247-265.
[15] PEACEMAN D H, Jr RACHFORD H H. The numerical solution of parabolic elliptic differential equations[J]. Journal of the Society for Industrial and Applied Mathematics, 1955, 3(1):28-41.
[16] GABAY D, MERCIER B. A dual algorithm for the solution of nonlinear variational problems via finite element approximations[J]. Computers and Mathematics with Applications, 1976, 2(1):17-40.
[17] YANG J F, ZHANG Y. Alternating direction algorithms for l₁-problems in compressive sensing[J]. SIAM Journal on Scientific Computing, 2011, 33(1):250-278.
[18] MA S Q, YIN W T, ZHANG Y, et al. An efficient algorithm for compressed MR imaging using total variation and wavelets[C]//CVPR 2008:Proceedings of the 2008 IEEE Conference on Computer Vision and Pattern Recognition. Washington, DC:IEEE Computer Society, 2008:1-8.
[19] YANG J F, ZHANG Y, YIN W T. A fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4(2):288-297.
[20] MOREAU J J. Fonctions convexes duales et points proximaux dans un espace hilbertien[J]. Comptes Rendus Hebdomadaires des Séances de Lacadémie des Sciences, 1962, 255:2897-2899.
[21] BURGER M, SAWATZKY A, STEIDL G. First order algorithms in variational image processing[M]//GLOWINSKI R, OSHER S J, YIN W T. Splitting Methods in Communication, Imaging, Science, and Engineering. Cham:Springer, 2016:345-407.
[22] DAUBECHIES I, DEFRISE M, de MOL C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J]. Communications on Pure and Applied Mathematics, 2003, 57(11):1413-1457.
[23] BECK A, TEBOULLE M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J]. SIAM Journal on Imaging Sciences, 2009, 2(1):183-202.
[24] HUANG J Z, ZHANG S T, METAXAS D. Efficient MR image reconstruction for compressed MR imaging[J]. Medical Image Analysis, 2011, 15(5):670-679.
[25] CHEN C, LI Y Q, AXEL L, et al. Real time dynamic MRI by exploiting spatial and temporal sparsity[J]. Magnetic Resonance Imaging, 2016, 34(4):473-482.
[26] BECK A, TEBOULLE M. Smoothing and first order methods:a unified framework[J]. SIAM Journal on Optimization, 2012, 22(2):557-580.
[27] BAUSCHKE H H, COMBETTES P L. Convex Analysis and Monotone Operator Theory in Hilbert Spaces[M]. Berlin:Springer, 2011:399-413.
[28] EHRHATDT M J, BETCKE M M. Multi-contrast MRI reconstruction with structure-guided total variation[J]. SIAM Journal on Imaging Science, 2016, 9(3):1084-1106.

Proximal smoothing iterative algorithm for magnetic resonance image reconstruction based on Moreau-envelope

基于Moreau-包络的近似平滑迭代磁共振图像重建算法

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

[1]	WANG Daiwei, XU Gaochao, LI Long. Task allocation strategy in unmanned aerial vehicle-assisted mobile edge computing [J]. Journal of Computer Applications, 2021, 41(10): 2928-2936.
[2]	ZHANG Yanjiao, QIAO Zhiwei. High-precision sparse reconstruction of CT images based on multiply residual UNet [J]. Journal of Computer Applications, 2021, 41(10): 2964-2969.
[3]	XI Yarui, QIAO Zhiwei, WEN Jing, ZHANG Yanjiao, YANG Wenjing, YAN Huiwen. High order TV image reconstruction algorithm based on Chambolle-Pock algorithm framework [J]. Journal of Computer Applications, 2020, 40(6): 1793-1798.
[4]	YANG Libo, JIANG Tiegang, XU Zhiqiang. Hybrid gradient based hard thresholding pursuit algorithm [J]. Journal of Computer Applications, 2020, 40(3): 912-916.
[5]	ZHAO Yongzhu, LI Weidong, TANG Bin, MEI Feng, LU Wenda. Efficient storage scheme for deadline aware distributed matrix multiplication [J]. Journal of Computer Applications, 2020, 40(2): 311-315.
[6]	ZONG Chunmei, ZHANG Yueqin, CAO Jianfang, ZHAO Qingshan. Compressed sensing magnetic resonance imaging based on deep priors and non-local similarity [J]. Journal of Computer Applications, 2020, 40(10): 3054-3059.
[7]	DU Xiaolei, CHEN Zhigang, ZHANG Nan, XU Xu. Train fault identification based on compressed sensing and deep wavelet neural network [J]. Journal of Computer Applications, 2019, 39(7): 2175-2180.
[8]	YU Yun, LIAN Xiaocan, ZHU Yuhang, TAN Guoping. Resource allocation optimization method for augment reality applications based on mobile edge computing [J]. Journal of Computer Applications, 2019, 39(1): 22-25.
[9]	QIAO Jianhua, ZHANG Xueying. Compressive data gathering based on even clustering for wireless sensor networks [J]. Journal of Computer Applications, 2018, 38(6): 1691-1697.
[10]	ZHANG Yanfeng, FAN Xi'an, YIN Zhiyi, JIANG Tiegang. Backtracking-based conjugate gradient iterative hard thresholding reconstruction algorithm [J]. Journal of Computer Applications, 2018, 38(12): 3580-3583.
[11]	GAO Ya, ZHANG Hailin, LU Xiaofeng. Statistical quality of service driven optimal power allocation in energy harvesting based wireless networks [J]. Journal of Computer Applications, 2018, 38(1): 212-216.
[12]	JIN Yong, GONG Shengli. Cluster-based resource allocation scheme in dense femtocell network [J]. Journal of Computer Applications, 2018, 38(1): 217-221.
[13]	QIAO Jianhua, ZHANG Xueying. Compressed sensing based data gathering in wireless sensor networks: a survey [J]. Journal of Computer Applications, 2017, 37(11): 3261-3269.
[14]	LI Xin, CUI Ziguan, SUN Linhui, ZHU Xiuchang. Image super-resolution reconstruction based on local regression model [J]. Journal of Computer Applications, 2016, 36(6): 1654-1658.
[15]	WU Jianning, XU Haidong, LING Yun, WANG Jiajing. Human activity pattern recognition based on block sparse Bayesian learning [J]. Journal of Computer Applications, 2016, 36(4): 1039-1044.