基于Moreau-包络的近似平滑迭代磁共振图像重建算法  

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

作　　者：刘晓晖 路利军[1] 冯前进[1] 陈武凡[1] LIU Xiaohui;LU Lijun;FENG Qianjin;CHEN Wufan(School of Biomedical Engineering,Southern Medical University,Guangzhou Guangdong 510515,China)

机构地区：[1]南方医科大学生物医学工程学院,广州510515

出　　处：《计算机应用》2018年第7期2076-2082,共7页journal of Computer Applications

基　　金：国家重点研发专项(2016YFC0104003);国家自然科学基金资助项目(81501541)~~

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。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.

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 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TP751.1[自动化与计算机技术—计算机科学与技术]