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

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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。

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	蒋明峰
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关键词 ：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).

Key words： Magnetic Resonance Imaging (MRI) Compressed Sensing(CS) Total Variation (TV) extension method Group-sparsity

收稿日期: 2015-02-02 出版日期: 2015-07-17

PACS:

R445.2

基金资助:

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

通讯作者: 蒋明峰：男，1977年生，副教授，博士，硕士生导师，研究方向为计算机医学图像处理、生物医学信号处理. E-mail: m.jiang@zstu.edu.cn

作者简介: 蒋明峰：男，1977年生，副教授，博士，硕士生导师，研究方向为计算机医学图像处理、生物医学信号处理. 刘渊：男，1991年生，硕士生，研究方向为计算机图像处理. 徐文龙：男，1972年生，教授，博士，硕士生导师，研究方向为生物医学信号处理、磁共振图像处理. 冯杰：男，1980年生，讲师，博士，研究方向为视频图像处理. 汪亚明：男，1972年生，教授，博士，博士生导师，研究方向为模式识别、图像处理.

引用本文:

蒋明峰,刘渊,徐文龙,冯杰,汪亚明. 基于全变分扩展方法的压缩感知磁共振成像算法研究[J]. 电子与信息学报, 2015, 37(11): 2608-2612. Jiang Ming-feng, Liu Yuan, Xu Wen-long, Feng Jie, Wang Ya-ming. The Study of Compressed Sensing MR Image Reconstruction Algorithm Based on the Extension of Total Variation Method. JEIT, 2015, 37(11): 2608-2612.

链接本文:

http://jeit.ie.ac.cn/CN/10.11999/JEIT150179 或 http://jeit.ie.ac.cn/CN/Y2015/V37/I11/2608

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