核范数极小化改进算法及其动态磁共振图像重建应用研究

发布时间：2018-02-27 10:41

本文关键词： 磁共振成像动态磁共振成像图像重建核范数极小化交替方向法低秩模型　出处：《南京邮电大学》2015年硕士论文　论文类型：学位论文

【摘要】：动态磁共振成像技术是一项重要的医学研究和诊断技术,动态磁共振成像存在扫描时间较长的缺点,导致病人无法忍受长时间扫描而发生不自觉的运动,这影响医学图像重建质量。临床应用中,通过提高主磁场强度、梯度场强度等相关的物理方法来缩短成像时间,现已达到应用极限,必须寻找更有效的数学方法提高重建速度。为此,在磁共振成像技术研究中,如何快速重建获得清晰图像尤为重要。本论文将低秩描述引入动态磁共振图像的重建过程,将每帧作为时空矩阵的列,利用时空相关性获得低秩矩阵。低秩矩阵通过核范数极小化求解,本论文针对大规模图像序列数据,在交替方向法框架下研究核范数极小化改进算法,并对动态磁共振图像重建的一阶优化算法进行深入研究。核范数极小化迭代算法涉及奇异值分解,计算复杂度高,本论文采用低秩矩阵分解方法来求解核范数,先将数据矩阵分解为两个低秩数据矩阵乘积,将约束条件转化为增广拉格朗日函数,分块极小化求解。算法避免了每次迭代的奇异值分解,降低了算法的复杂度。矩阵填充实验表明该方法大大提高了核范数极小化的运行效率。针对动态磁共振图像的核范数近似梯度重建模型,目标函数含有数据拟合项和核范数,该方法基于核范数极小化先验信息和加速近似梯度算法,通过求解核范数正则化线性最小二乘问题完成图像的重建。PINCAT数据和临床心脏灌注磁共振成像数据仿真实验,表明本模型下的改进算法重建效果良好。针对动态磁共振图像的低秩与稀疏分解重建模型,目标函数含有数据拟合项、核范数和L1范数,该方法基于低秩加稀疏先验知识,通过交替方向法求解正则化逆问题,来完成图像重建。幻影模拟数据和真实心脏磁共振数据仿真实验,表明本模型下的改进算法有较好的图像重建效果,较高的计算效率。
[Abstract]:Dynamic magnetic resonance imaging is an important medical research and diagnosis technique. Dynamic magnetic resonance imaging has the disadvantage of long scanning time, which results in patients unable to endure long scanning and unconsciously moving. This affects the quality of medical image reconstruction. In clinical application, the imaging time can be shortened by increasing the intensity of the main magnetic field and the intensity of the gradient field. It is necessary to find more effective mathematical methods to improve the reconstruction speed. Therefore, in the research of magnetic resonance imaging, it is very important to obtain clear image quickly. In this paper, the low rank description is introduced into the reconstruction process of dynamic magnetic resonance image. Each frame is regarded as the column of space-time matrix, and the low-rank matrix is obtained by space-time correlation. The low-rank matrix is solved by kernel norm minimization. The improved kernel norm minimization algorithm is studied in the framework of alternating direction method, and the first-order optimization algorithm for dynamic magnetic resonance image reconstruction is studied in depth. The kernel norm minimization iterative algorithm involves singular value decomposition (SVD) and has high computational complexity. In this paper, the low rank matrix decomposition method is used to solve the kernel norm. Firstly, the data matrix is decomposed into the product of two low rank data matrices, and the constraint condition is transformed into an augmented Lagrangian function. The algorithm avoids the singular value decomposition of each iteration. The algorithm complexity is reduced. Matrix filling experiment shows that this method greatly improves the running efficiency of kernel norm minimization. For the kernel norm approximate gradient reconstruction model of dynamic magnetic resonance image, the objective function contains data fitting term and kernel norm. Based on the priori information of kernel norm minimization and the accelerated approximate gradient algorithm, the simulation experiments of image reconstruction. PINCAT data and clinical cardiac perfusion magnetic resonance imaging data are completed by solving the kernel norm regularization linear least squares problem. The result shows that the improved algorithm has good reconstruction effect. For the low rank and sparse decomposition reconstruction model of dynamic magnetic resonance image, the objective function contains data fitting items, kernel norm and L1 norm. The method is based on low rank and sparse prior knowledge. The simulation experiments of phantom simulated data and real cardiac magnetic resonance data show that the improved algorithm has better image reconstruction effect and higher computational efficiency.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TP391.41;R445.2

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