非均匀磁共振压缩成像的交替方向乘子法  

Alternating direction method of multipliers for non-uniform MR compressive imaging

作　　者：袁太文 谢永乐[2] 毕东杰[2] Yuan Taiwen;Xie Yongle;Bi Dongjie(School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China;School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China)

机构地区：[1]电子科技大学机械与电气工程学院,成都611731 [2]电子科技大学自动化工程学院,成都611731

出　　处：《仪器仪表学报》2018年第3期223-230,共8页Chinese Journal of Scientific Instrument

摘　　要：为了缩短磁共振成像的扫描时间、提高成像质量,提出一种在压缩感知框架下的非均匀磁共振压缩图像交替方向乘子算法。该方法联合考虑磁共振成像（MRI）图像在变换域和梯度域下的稀疏性,并使用非均匀傅里叶变换实现插值处理,在此基础上构建出MRI图像重构模型,然后采用交替方向乘子法求解该模型。该算法引入辅助变量,将原始模型中的优化问题分解为更容易求解的子优化问题,再使用交替方向最小化方法分别求解。通过一个乐高积木和一个老鼠心脏的径向MRI压缩成像实验来验证算法的有效性。实验中利用磁共振图像从5%到30%（步进为1%）的欠采样数据进行图像重建,并采用重构图像与原始图像的结构相似度评价重构图像质量,结果显示基于该方法的压缩成像算法重构图像质量显著优于基于回溯线搜索的共轭梯度法的重构图像。同时,以峰值信噪比作为图像质量的评价指标对两种算法下的老鼠心脏重构图像进行比较,依然得到相同的结论。In order to shorten the scanning time and improve the imaging quality of magnetic resonance imaging（MRI）,an alternating direction algorithm of multipliers for non-uniform MR compressive image under compressed sensing framework is proposed in this paper.This algorithm jointly considers the sparseness of the MRI image in transform domain and gradient domain.The non-uniform Fourier transform is used to implement interpolation processing.Based on above,the MRI image reconstruction model is built.Then,an efficient algorithm referred to the alternating direction method of multipliers is used to solve the model.In this algorithm,the auxiliary variables are introduced,and the optimization problem in original model is decomposed into several easier solved sub-optimization problems.Then,these sub-optimization problems are solved with alternating direction minimization method.The experiments on the MRI image of a Lego building block and a living mouse cardiac radial MRI image obtained from the Varian Unity Inova MRI system were used to verify the effectiveness of algorithm.In these experiments,the images were reconstructed from the MRI data with under-sampling rates from 5% to 30%（step of 1%） using different algorithms.The structural similarity image metric of the reconstructed image and original image is used to evaluate the qualities of the reconstructed images,the results show that the image reconstruction quality of the compressed imaging algorithm based on the proposed method is obviously better than that of the conjugate gradient method based on backtracking line search.At the same time,taking the peak signal to noise ratio as image quality evaluation index,the cardiac reconstruction images in living mouse cardiac experiment for the two algorithms were compared,the same conclusion is still obtained.

关 键 词：磁共振成像 压缩感知 交替方向乘子法 非均匀快速傅里叶变换 图像结构相似度 

分 类 号：Q-334[生物学] TP181[自动化与计算机技术—控制理论与控制工程]