改进的共轭梯度MRI压缩成像算法
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摘要
为了缩短磁共振成像系统的扫描时间,压缩感知方法利用欠采样数据和非线性恢复算法实现系统的实时或准实时成像需求。通过联合考虑MRI图像在变换域和梯度域下的稀疏性,提出了一种基于预测线搜索方法的共轭梯度算法来重建磁共振图像。针对共轭梯度算法中线搜索次数过多和运行时间过长问题,采用基于预测的方法来优化搜索步长值,以此缩短算法执行时间和减少线搜索次数。仿真实验利用磁共振图像的10%、20%和30%的下采样数据进行图像重建,结果显示基于该预测线搜索方法的压缩成像算法执行时间少于回溯线搜索法的执行时间,重构图像质量优于零填充法和FR共轭梯度法,验证了该算法的有效性。
In order to shorten the scanning time of magnetic resonance imaging(MRI), a combination of sub-nyquist sampling data and nonlinear reconstruction algorithms is adopted in the compressed sensing method to realize the real-time or quasi real-time imaging requirement. Considering the sparseness of MRI images in the transform domain and the gradient domain, a conjugate gradient algorithm is proposed to reconstruct the magnetic resonance image using the prediction line search method. The conventional conjugate gradient algorithm suffers a long computation time because of too many attempts in the line search process. We address this problem by optimizing the searching step size with a prediction approach, which significantly reduces the line search cost and accelerates convergence. Simulation results, with under-sampling rate at 10%, 20% and 30%, show that the prediction line search method achieves the best image reconstruction resolution in comparison to the zero filling method and the FR conjugate gradient method, while its time cost is less than the backtracking line search method, which illustrate the effectiveness of the proposed algorithm.
In order to shorten the scanning time of magnetic resonance imaging(MRI), a combination of sub-nyquist sampling data and nonlinear reconstruction algorithms is adopted in the compressed sensing method to realize the real-time or quasi real-time imaging requirement. Considering the sparseness of MRI images in the transform domain and the gradient domain, a conjugate gradient algorithm is proposed to reconstruct the magnetic resonance image using the prediction line search method. The conventional conjugate gradient algorithm suffers a long computation time because of too many attempts in the line search process. We address this problem by optimizing the searching step size with a prediction approach, which significantly reduces the line search cost and accelerates convergence. Simulation results, with under-sampling rate at 10%, 20% and 30%, show that the prediction line search method achieves the best image reconstruction resolution in comparison to the zero filling method and the FR conjugate gradient method, while its time cost is less than the backtracking line search method, which illustrate the effectiveness of the proposed algorithm.
引文
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[3]王水花,张煜东.压缩感知磁共振成像技术综述[J].中国医学物理学杂志,2015,32(2):158-162.WANG Shui-hua,ZHANG Yu-dong.Survey on compressed sensing magnetic resonance imaging technique[J].Chinese Journal of Medical Physics,2015,32(2):158-162.
[4]RUNGE V M,RICHTER J K,HEVERHAGEN J T.Speed in clinical magnetic resonance[J].Investigative Radiology,2017,52(1):1-17
[5]翁卓,谢国喜,刘新,等.基于k空间加速采集的磁共振成像技术[J].中国生物医学工程学报,2010,29(5):785-790.WENG Zhuo,XIE Guo-xi,LIU Xin,et al.Development of fast magnetic resonance imaging techniques based on k-space accelerated collection[J].Chinese Journal of Biomedical Engineering,2010,29(5):785-790.
[6]DAVID L D.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[7]SOUSSEN C,GRIBONVAL R,IDIER J,et al.Joint K-step analysis of orthogonal matching pursuit and orthogonal least squares[J].IEEE TransInform Theory,2013,59(5):3158-3174.
[8]BLUMENSATH T,DAVIES M E.Iterative hard thresholding for compressed sensing[J].Applied and Computational Harmonic Analysis,2009,27(3):265-274.
[9]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.
[10]YANG Xia-han,ZHENG Y R,Yang M,et al.Compressed sensing with non-uniform fast fourier transform for radial Ultra-short Echo Time(UTE)MRI[C]//2015 IEEE 12th International Symposium on Biomedical Imaging(ISBI).New York,USA:IEEE,2015,1:918-921.
[11]BI Dong-jie,MA Lan,XIE X,et al.A splitting bregman-based compressed sensing approach for radial UTE MRI[J].IEEE Transaction on Applied Superconductivity,2016,26(7):1-5.
[12]JAING Xiao-ping,DING Hao,ZHANG Hua,et al.Study on compressed sensing reconstruction algorithm of medical image based on curvelet transform of image block[J].Neurocomputing,2017,220:191-198.
[13]CHEN S S,DAVID L D,SAUNDERS M A.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,2001,43(1):129-159.
[14]RUDIN L,OSHER S,FATEMI E.Non-linear total variation noise removal algorithm[J].Physica D,1992,60:259-268.
[15]WILLIAN W H,ZHANG Hong-chao.A survery of nonlinear conjugate gradient methods[J].Pacific Journal of Optimization,2006,2(1):35-58.
[16]FLETCHER R,REEVES C.Function minimization by conjugate gradients[J].Computer Journal,1964,7(2):149-154.
[17]DAI Y H,YUAN Y.A nonlinear conjugate gradient method with a strong global convergence property[J].SIAMJournal on Optimization,1999,10(1):177-182.
[18]LU Ai-guo,LIU Hong-wei,ZHENG X,et al.A variant spectral-type FR conjugate gradient method and its global convergence[J].Applied Mathematics and Computation,2011,217(12):5547-5552.
[19]FATEMI M.A new efficient conjugate gradient method for unconstrained optiomization[J].Journal of Computational&Applied Mathematics,2016,300:207-216.
[20]SHEPP L A,LOGAN B F.The fourier reconstruction of a head section[J].IEEE Transactions on Nuclear Science,1974,21(3):21-43.
[21]WANG Z,BOVIK A C,SHEIKH H R,et al.Image quality assessment:from error visibility to structural similarity[J].IEEE Transactions on Image Process,2004,13(4):600-612.