Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (8): 28-35.DOI: 10.3778/j.issn.1002-8331.1801-0104

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Proximal iterative reconstruction algorithm for MR images based on primal-dual framework

LIU Xiaohui, ZHANG Xinyuan, LU Lijun, FENG Qianjin, CHEN Wufan   

  1. School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China
  • Online:2018-04-15 Published:2018-05-02

磁共振图像的原始-对偶近似迭代重建算法

刘晓晖,张鑫媛,路利军,冯前进,陈武凡   

  1. 南方医科大学 生物医学工程学院,广州 510515

Abstract: Compressed Sensing(CS) based Magnetic Resonance Imaging(MRI) is a fast imaging technology which exploits the sparsity of Magnetic Resonance(MR) images. In view of the linear composite regularization term in the canonic reconstruction model for CS-MRI, a primal-dual iterative reconstruction algorithm is proposed which solves augmented Lagrangian of the primal and dual problems iteratively. The Moreau envelope is utilized to cope with the non-smooth regularization terms followed by a gradient calculation step using the approximate operator. Experiment results of phantom and real MR images show that compared with Conjugate Gradient algorithm(CG), operator splitting algorithm(TVCMRI), variable splitting algorithm (RecPF) and fast composite splitting algorithm(FCSA), the algorithm gives the best reconstruction effect. In addition, the algorithm complexity compares favorably with FCSA which is the fastest algorithm so far.

Key words: fast magnetic resonance imaging, compressed sensing, primal-dual, approximate operator

摘要: 基于压缩感知(CS)的磁共振成像(MRI)是一种利用磁共振(MR)图像的稀疏性的快速成像技术,经典CS-MRI重建数学模型是在包含线性合成非平滑正则约束下的最优化问题。针对重建模型中的线性合成正则项提出利用原始-对偶框架同时求解原始-对偶问题,对原始-对偶问题的增广Lagrangian形式求解其最优解,提出了一种原始-对偶迭代重建算法;对于非平滑正则项的处理,提出使用Moreau包络进行平滑近似,然后利用近似算子得到平滑近似函数的导数形式。用体模图像和真实MR图像,与共轭梯度算法(CG)、算子分离算法(TVCMRI)、变量分离算法(RecPF)和快速混合分离算法(FCSA)进行比较,表明该算法重建效果最好,算法复杂度与最快的FCSA算法相当。

关键词: 快速磁共振成像, 压缩感知, 原始-对偶, 近似算子