一种基于全变分正则化低秩稀疏分解的动态MRI重建方法

针对应用迭代软阈值(IST)算法对基于低秩稀疏矩 阵(L＋S,low rank and sparse)分解模型的动态磁共振成像(MRI)图像 进行重建存在重建精度一般和重建速度慢的问题,提出在矩阵L＋S分解模 型的基础上引入全变分(TV)正则项,达到进一步去噪声和去伪影,提高重建精度目的；利用 非精确增广拉 格朗日算法(IALM)达到快速重建的目的。通过对心脏灌注动态MRI成像和心电影MRI成 像的仿真实 验表明:对于L＋S低秩稀疏矩阵分解模型的重建,IALM比IS T算法速度更快,精度更高；模型引入TV正则项 后再利用IALM重建,重建速度虽然比之前的IALM有所降低,但依然优于IST算法, 并且重建精 度高于之前的IALM。在L＋S分解模型中引入TV正则项 提高了MRI重建精度,运用IALM进行求解加快了重建速度,结合TV正则项和IALM达到了 快速、高精度重建的目的。

A total variation regularization low-rank and sparse matrix decomposition based reconstruction method of dynamic MRI images

The application of iterative soft threshold (IST) algorithm for dynamic magnetic resonance imaging (MRI) image reconstruction based on low-rank and sparse matrix decomposition exists two problems of the poor reconstruction accuracy and conver ge speed.Considering these problems,total variation (TV) regularization based on low-rank and sparse matrix decomposition model is introduced to further remove noise and artifacts.Besides, inexact augmented Lagrangian method (IALM) is used for fast reconstruction.In order to verify the effectiveness of the proposed method,the simulations about reconstruc tion of cardiac perfusion MRI and cardiac cine MRI are done.The results of the simulation demonstrate that: using IALM for low-rank and sparse matrix decomposition reconstruction results in better reconstruction performance than using IST method.Although introducing TV regularization reduces the reconstruction speed compared with IALM,it still fast than IST,and the recon struction accuracy is higher than that of IALM.So introducing TV regularization to the low-rank a nd sparse matrix decomposition model can improve the MRI reconstruction accuracy,and using IALM a lgorithm can speed up the reconstruction speed.The combination of TV regularization and IALM algor ithm has achieved the purpose of rapid and high precision reconstruction.