基于复合正则化的高效压缩感知磁共振成像研究

doi:10.3969/j.issn.1006-2475.2016.05.007

摘要/Abstract

摘要：

压缩感知磁共振成像可以在实现数据扫描加速的同时不降低成像质量。在压缩感知磁共振成像方法中，当前的复合正则化重建模型极少根据信号包含的各种各样的结构特征个性化选取不同的正则

化方法，使得当前成像方法需要较高的采样率以获得具有医学诊断价值的图像。基于此，本文提出一种新的复合正则化成像模型，该模型根据曲波变换域高低频子带系数的不同结构特征全变分正则化图

像灰度值和低频系数，l1范数正则化高频系数并采用k空间观测值约束成像保真度。采用变量分裂与交替方向乘子法求解该成像模型。针对活体数据的实验仿真结果表明，在相同采样率下，本文所

提方法重构性能远优于当前基于小波与全变分的正则化模型。

关键词: 压缩感知, 磁共振成像, 均匀离散曲波变换, 变量分裂, 交替方向乘子法

Abstract:

Compressed sensing(CS) is well utilized to accelerate magnetic resonance imaging(MRI) without degrading images quality. The present compound regularization imaging

models seldom select different regularization tools according to the different structural features of images. The imaging methods thus require high sampling rates to obtain

images with diagnostic value. In this paper, a novel compound regularization CS MRI model integrating two regularization tools: uniform discrete curvelet transform and total

variation, is introduced. It includes spatial image and lowpass subband coefficients total variation regularization, highpass subbands coefficients l1

regularization and kspace data fidelity constraint. Then this CS MRI model formulation is solved via variable splitting and alternating direction method of multipliers.

Simulated results on in vivo data are evaluated by objective indices and visual perception, which indicates that the proposed method outperforms the existing regularization

models established on the total variation and wavelets under the same sampling rate.

Key words: compressed sensing, magnetic resonance imaging, uniform discrete curvelet transform, variable splitting, alternating direction method of multipliers

中图分类号:

TP301.6

申慧君. 基于复合正则化的高效压缩感知磁共振成像研究[J]. 计算机与现代化, 2016, 0(5): 39-45.

SHEN Huijun. Efficient Compressed Sensing Magnetic Resonance Imaging #br# Based on Compound Regularization[J]. Computer and Modernization, 2016, 0(5): 39-45.

［1］Donoho D L. Compressed sensing［J］. IEEE Transactions on Information Theory, 2006,52(4):1289-1306.
［2］Gitta Kutyniok. Compressed sensing: Theory and applications［J］. Corr, 2012,52(4):1289-1306.
［3］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.
［4］Lustig M, Donoho D L, Santos J M, et al. Compressed sensing MRI［J］. Signal Processing Magazine, IEEE, 2008,25(2):72-82.
［5］Chen Yunmei, Ye Xiaojing, Huang Feng. A novel method and fast algorithm for MR image reconstruction with significantly undersampled data［J］. Inverse Problems and

Imaging, 2010,4(2):223-240.
［6］Santos J M, Cunningham C H, Lustig M, et al. Single breathhold wholeheart MRA using variabledensity spirals at 3t［J］. Magnetic Resonance in Medicine, 2006,55

(2):371-379.
［7］Huang Junzhou, Zhang Shaoting, Metaxas D. Efficient MR image reconstruction for compressed MR imaging［J］. Medical Image Analysis, 2011,15(5):135-142.
［8］Huang Junzhou, Yang Fei. Compressed magnetic resonance imaging based on wavelet sparsity and nonlocal total variatio［C］// 2012 9th IEEE International Symposium on

Biomedical Imaging (ISBI). 2012:968-971.
［9］Do M N, Vetterli M. The contourlet transform: An efficient directional multiresolution image representation［J］. IEEE Transactions on Image Processing, 2005,14(12):2091-

2106.
［10］Da Cunha A L, Zhou Jianping, Do M N. The nonsubsampled contourlet transform: Theory, design, and applications［J］. IEEE Transactions on Image Processing, 2006,15

(10):3089-3101.
［11］Lu Yue, Do M N. A new contourlet transform with sharp frequency localization［C］// 2006 IEEE International Conference on Image Processing. 2006:1629-1632.
［12］Candes E, Demanet L, Donoho D, et al. Fast discrete curvelet transforms［J］. Multiscale Modeling & Simulation, 2006,5(3):861-899.
［13］Ning Bende, Qu Xiaobo, Guo Di, et al. Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and nonconvex

optimization［J］. Magnetic Resonance Imaging, 2013,31(9):1611-1622.
［14］Ravishankar S, Bresler Y. MR image reconstruction from highly undersampled kspace data by dictionary learning［J］. IEEE Transactions on Medical Imaging, 2011,30

(5):1028-1041.
［15］Qu Xiaobo, Guo Di, Ning Bende, et al. Undersampled MRI reconstruction with patchbased directional wavelets［J］. Magnetic Resonance Imaging, 2012,30(7):964-977.
［16］Awate S P, DiBella E V R. Spatiotemporal dictionary learning for undersampled dynamic MRI reconstruction via joint framebased and dictionarybased sparsity［C］//

2012 9th IEEE International Symposium on Biomedical Imaging (ISBI). 2012:318-321.
［17］Candes E J, Wakin M B, Boyd S P. Enhancing sparsity by reweighted l1 minimization［J］. Journal of FourierAnalysis and Applications, 2008,14(5-6):877-905.
［18］Yang Junfeng, Zhang Yin. Alternating direction algorithms for ＼ell_1problems in compressive sensing［J］. SIAM Journal on Scientific Computing, 2011,33(1):250-278.
［19］Manya V Afonso, Jose M BioucasDias, Mario A T Figueiredo. Fast image recovery using variable splitting and constrained optimization［J］. IEEE Transactions on Image

Processing, 2010,19(9):2345-2356.
［20］AfonsoM V, BioucasDias J M, Figueiredo M A T. An augmented Lagrangian approach to the constrained optimization formulation of imaging inverse problems［J］. IEEE

Transactions on Image Processing, 2011,20(3):681-695.

［21］Nguyen T T, Chauris H. Uniform discrete curvelet transform［J］. IEEE Transactions on Signal Processing, 2010,58(7):3618-3634.
［22］Ma Shiqian, Yin Wotao, Zhang Yin, et al. An efficient algorithm for compressed MR imaging using total variation and wavelets［C］// IEEE Conference on Computer Vision

and Pattern Recognition(CVPR 2008). 2008:1-8.
［23］Chen Chen, Huang Junzhou. Compressive sensing MRI with wavelet tree sparsity［C］// Advances in Neural Information Processing Systems. 2012:1115-1123.
［24］Qu Xiaobo, Hou Yingkun, Lam Fan, et al. Magnetic resonance image reconstruction from undersampled measurements using a patchbased nonlocal operator［J］. Medical Image

Analysis, 2014,18(6):843-856.
［25］Shin P J, Larson P E Z, Ohliger M A, et al. Calibrationless parallel imaging reconstruction based on structured lowrank matrix completion［J］.Magnetic Resonance in

Medicine, 2014,72(4):959-970.
［26］Candes E J, Donoho D L. Curvelets: ASurprisingly Effective Nonadaptive Representation for Objects with Edges［R］. Department of Statistics, Stanford University, 1999.
［27］Chambolle A. An algorithm for total variation minimization and applications［J］. Journal of Mathematical Imaging and Vision, 2004,20(12):89-97.
［28］Eckstein J, Bertsekas D P. On the DouglasRachford splitting method and the proximal point algorithm for maximal monotone operators［J］. Mathematical Programming,

1992,55(13):293-318.
［29］Qu Guihong, Zhang Dali, Yan Pingfan. Information measure for performance of image fusion［J］. Electronics Letters, 2002,38(7):313-315.

[1]	刘迅, 张东, 袁达龙. 基于形变场灰度场插值网络的切片间超分辨率[J]. 计算机与现代化, 2024, 0(03): 67-71.
[2]	杜鑫昌, 高瑜翔, 曹远杰, 张皓, 刘海波. 改进混沌方程及压缩感知理论图像加密算法[J]. 计算机与现代化, 2022, 0(04): 115-120.
[3]	张连娜, 张慧萍, 李荣鹏, 宋学力. 基于二次筛选的回溯广义正交匹配追踪算法的稀疏信号重构[J]. 计算机与现代化, 2022, 0(03): 111-115.
[4]	陈勋豪, 杨莹, 黄俊茹, 孙玉宝. 基于多尺度融合网络的视频快照压缩感知重建[J]. 计算机与现代化, 2021, 0(12): 58-64.
[5]	姚传文, 黄道斌, 叶明全, . 基于粗糙集自适应粒度的MR脑肿瘤图像分割[J]. 计算机与现代化, 2021, 0(01): 34-37.
[6]	金安安, 丁双双, 熊卿智, 许婷婷, 习淑萍, 马继忠. 基于SWOMP算法的EPMA影像优化重构[J]. 计算机与现代化, 2020, 0(12): 104-111.
[7]	张蕾, 崔娟娟, 李晶晶. WSN中基于压缩感知的分簇数据收集算法[J]. 计算机与现代化, 2020, 0(09): 1-5.
[8]	张欢1,2,雷宏1. 干扰恢复问题中惩罚优化方法相变现象分析[J]. 计算机与现代化, 2019, 0(06): 76-.
[9]	余红星1,2,申国伟1,2，郭春1，2. 一种基于自动特征工程与压缩感知的网络隧道检测方法[J]. 计算机与现代化, 2019, 0(06): 1-.
[10]	吴佳1，赵云2，张丽娟3，宋文2. 基于空时压缩感知算法的蜂窝流量预测[J]. 计算机与现代化, 2018, 0(12): 11-.
[11]	董袁泉1，王浩2. 基于离散鸡群压缩感知的WSNs多目标定位[J]. 计算机与现代化, 2017, 0(12): 23-27.
[12]	刘继承1，王敏莹1，李浩然2. 基于改进CoSaMP算法的图像重建[J]. 计算机与现代化, 2015, 0(5): 48-52.
[13]	陈宝深. 基于压缩感知技术的自适应阵列天线滤波系统的研究[J]. 计算机与现代化, 2013, 1(7): 98-100,.

基于复合正则化的高效压缩感知磁共振成像研究

Efficient Compressed Sensing Magnetic Resonance Imaging #br# Based on Compound Regularization

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 13

编辑推荐

Metrics

本文评价