二阶锥规划在MR图像重建中的应用研究

用传统MR图像重建方法对降采样数据进行重建往往会产生严重的伪影或导致重建图像的信噪比下降。用迭代重建算法对MR降采样数据进行优质重建,目标函数仅包含待重建图像的全变分,约束条件为一等式约束。在数值求解过程中,将优化问题转化为二阶锥规划问题,采用具有良好收敛性的对数障碍算法进行优化求解。在迭代过程中用图像的全变分信息自适应地决定对数障碍参数。实验结果表明,算法很好地克服了网格算法中的伪影问题,可以重建出高质量的MR图像。

Second order cone programming and its application in MR image reconstruction

Reconstructing MR images from under-sampled measurement data using traditional reconstruction methods usually results in image artifacts and low signal to noise ratio.In this paper,an iterative MR image reconstruction algorithm is proposed.The objective function only includes the total variation of the image to be reconstructed.The optimization problem is converted to the second order cone programming and a log-barrier algorithm is used.In the optimization process,the barrier parameter is adaptively defined by the total variation of the reconstructed images in the process of iteration.The experimental results achieve high image quality with significantly fewer image artifacts as compared with the conventional gridding algorithm.