基于凸集投影的稀疏磁共振图像重建新算法  

New Algorithm for Sparse MRI Reconstruction Based on POCS Optimization

作　　者：刘平[1] 冯衍秋[1] 陈武凡[1] 

机构地区：[1]南方医科大学生物医学工程学院,广东广州510515

出　　处：《中国医学物理学杂志》2009年第3期1160-1162,1179,共4页Chinese Journal of Medical Physics

基　　金：国家自然科学基金项目(No.30800254;No.30730036);广东省自然科学基金项目(No.06301304)。

摘　　要：目的:只将稀疏MRI数据重建公式中的正则化项作为最小化的目标函数,避免在迭代过程中系统矩阵参与运算,以降低算法的运算量,提高稀疏MRI数据重建的速度。方法:本文中所用的正则化函数是图像全变分与小波系数L1范数的组合,其最小化问题是用次梯度优化算法来求解的。在每一步迭代过程中,首先求出正则化项的次梯度,用次梯度优化算法求解得到中间图像并对其进行傅立叶变换,再根据凸集投影原理,直接将在相位编码方向上随机降采样的K空间数据替换到中间图像频域值的相应位置上,然后对替换后得到的频域值进行反傅立叶变换并将求得的图像作为下一次迭代过程的初始图像。结果:在正则化函数和迭代步数均相同的条件下,本文方法重建的图像质量与NCG-SMRI方法的相当,但重建速度是NCG-SMRI方法的2倍多。结论:实验表明,在不降低重建图像的质量的前提下,本文方法可以提高稀疏MRI数据的重建速度,能进一步满足临床上对MRI重建速度的要求。Objective： In order to reduce the amotmt of computation and improve the reconstruction speed, we only regard the regularization fimctional as the objective functional to be minimized in the process of reconstruction of sparse MR/ data, which can avoids using system matrix during the process of computation. Methods： The regularization functional used in this article is the combination between image＇s total variation and L1 norm of image＇s wavelet coefficients, and the problem of its minimization is solved by subgradient method. In each iterative step, the subgradient of regularization functional is calculated first, then subgradient method is used to find the intermediate image. After that, we calculate the fourier transform of the intermediate image, and then, according to the principle of POCS, directly replace its corresponding frequency values with the measured K-space data which is sparsely sampled along the direction of phase-encoding randomly, and then take the inverse fourier transform of the frequency values after replacement and use the reconstructed image as the initial image for next itera- tive. Results： Under the condition of the same iterative number and the same regularization functional, the quantity of images reconstructed by our method is nearly the same as that of NCG-SMR/method, but our method＇s speed is two more times than that NCG-SMRI method＇s. Conclusions： The experiment shows that our method can increase the speed of sparse MRI data reconstruction while ensuring the quantity of the reconstructed images, which can meets the clinical requirements on MR/imaging speed further.

关 键 词：磁共振成像 凸集投影 稀疏数据 笛卡尔采样 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]