基于全变分扩展方法的压缩感知磁共振成像算法研究

蒋明峰; 刘渊; 徐文龙; 冯杰; 汪亚明

doi:10.11999/JEIT150179

基于全变分扩展方法的压缩感知磁共振成像算法研究

doi: 10.11999/JEIT150179

1.
(浙江理工大学信息学院杭州 310018) ②(中国计量学院生物医学工程系杭州 310018)

基金项目:

国家自然科学基金(61272311)，浙江省自然科学基金(LY14F010022, LZ15F020004)，浙江省科技厅公益项目(2013C31021, 2015C31075)，浙江省科技厅国际科技合作研究项目(2013C24019)，浙江省仪器科学与技术重中之重学科开放基金和浙江理工大学521人才培养计划

计量
- 文章访问数: 1645
- HTML全文浏览量: 165
- PDF下载量: 737
- 被引次数: 0
出版历程
- 收稿日期: 2015-02-02
- 修回日期: 2015-06-01
- 刊出日期: 2015-11-19

The Study of Compressed Sensing MR Image Reconstruction Algorithm Based on the Extension of Total Variation Method

1.
(School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)
2.
(School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)

Funds:

The National Natural Science Foundation of China (61272311)

摘要

摘要: 针对全变分算法在压缩感知磁共振成像(CS-MRI)重构过程中存在阶梯效应的问题，该文研究3种基于全变分扩展方法的CS-MRI成像算法，即高阶全变分、总广义变分和组合稀疏全变分，并将其与平移不变离散小波稀疏基相结合，建立稀疏模型，采用快速复合分裂算法求解CS-MRI重构的凸优化问题。同时，讨论了全变分及其扩展方法对两种不同磁共振图像数据和径向欠采样模式重构CS-MRI的精度。实验结果表明，基于全变分扩展的重构算法能有效解决全变分重建中存在阶梯效应的缺点；另外，相比高阶全变分和总广义变分重构算法，组合稀疏全变分方法具有更好的重建效果，获得更高重构信噪比。
- 磁共振图像 /
- 压缩感知 /
- 全变分扩展算法 /
- 组合稀疏
Abstract: The Total Variation (TV) method is often used to reconstruct the Compressed Sensing Magnetic Resonance Imaging (CS-MRI), however, it can generate the stair effect in the reconstructed MR image. In this paper, there types of TV extension based methods, i.e. High Degree Total Variation (HDTV), Total Generalize Variation (TGV) and Group-Sparsity Total Variation (GSTV), are proposed to implement the sparse reconstruction of MR image. In addition, the shift-invariant discrete wavelet transform are integrated into these TV extension based methods as the sparsifying transform. The Fast Composite Splitting Algorithm (FCSA) is adopted to solve the convex optimization problem of CS-MRI reconstruction. And the Two different types of MR images with radial sampling trajectory are used to validate the reconstruction performance of CS-MRI by using the TV extension methods. The experiment results show that the TV extension based models can overcome the shortcomings of TV based model. Moreover, compared with HDTV and TGV methods, the GSTV method can obviously improve the reconstruction quality with higher Signal-to-Noise Ratio (SNR).
- Magnetic Resonance Imaging (MRI) /
- Compressed Sensing(CS) /
- Total Variation (TV) extension method /
- Group-sparsity

HTML全文

参考文献(18)

Cands E J, Romberg J, and Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489-509.

Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.

娄静涛, 李永乐, 谭树人, 等. 基于全变分的全向图像稀疏重构算法[J]. 电子学报, 2014, 44(2): 243-249.

Lou Jing-tao, Li Yong-le, Tan Shu-ren, et al.. Sparse reconstruction for omnidirectional image based on total variation[J]. Acta Electronica Sinica, 2014, 44(2): 243-249.

李然, 干宗良, 崔子冠, 等. 联合时空特征的视频分块压缩感知重构[J]. 电子与信息学报, 2014, 36(2): 285-292.

Li Ran, Gan Zong-liang, Cui Zi-guan, et al.. Block compressed sensing reconstruction of video combined with temporal-spatial characteristics[J]. Journal of Electronics Information Technology, 2014, 36(2): 285-292.

Lustig M, Donoho D L, and Pauly J M. Sparse MRI: the application of compressed sensing for rapid MR Imaging[J]. Magnetic Resonance in Medicine, 2007, 58(6): 1182-1195.

Hu Y and Jacob M. Higher Degree Total Variation (HDTV) regularization for image recovery[J]. IEEE Transactions on Image Processing, 2012, 21(5): 2559-2571.

Guo W, Qin J, and Yin W. A new detail-preserving regularity scheme[J]. SIAM Journal on Imaging Sciences, 2014, 7(2): 1309-1334.

Selesnick I W and Chen P. Total variation denoising with overlapping group sparsity[C]. IEEE International Conference Acoust, Speech, Signal Processing (ICASSP), Vancouver, Canada, 2013: 1-5.

Zhang S, Block K T, and Frahm J. Magnetic resonance imaging in real time: advances using radial FLASH[J]. Journal of Magnetic Resonance Imaging, 2010, 31(1): 101-109.

Huang J, Zhang S, and Metaxas D. Efficient MR image reconstruction for compressed MR imaging[J]. Medical Image Analysis, 2011, 15(5): 670-679.

Ning B, Qu X, Guo D, 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.

Qu X, Hou Y, Lam F, et al.. Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator[J]. Medical Image Analysis, 2014, 18(6): 843-856.

Jiang M , Jin J, Liu F, et al.. Sparsity-constrained SENSE reconstruction: an efficient implementation using a fast composite splitting algorithm[J]. Magnetic Resonance Imaging, 2013, 31(7): 1218-1227.

Figueiredo M, Bioucas-Dias J, and Nowak R. Majorization minimization algorithms for wavelet-based image restoration[J]. IEEE Transactions on Image Processing, 2007, 16(12): 2980-2991.

He B, Liao L Z, Han D, et al.. A new inexact alternating directions method for monotone variational inequalities[J]. Mathematical Programming, 2002, 92(1): 103-118.

Jung H, Ye J C, and Kim E Y. Improved k-t BLAST and k-t SENSE using FOCUSS[J]. Physics in Medicine and Biology, 2007, 52(11): 3201-3226.

施引文献

资源附件(0)

访问统计