基于低秩稀疏分解快速算法的动态MRI重建

Dynamic MRI Reconstruction based on Low-rank Sparse Decomposition Fast Algorithm

通过低秩加稀疏矩阵分解模型重建欠采样动态磁共振图像时,常采用变量分裂算法来求解。针对共轭梯度法在二次项更新中迭代计算较为复杂的问题,为了加快重建速度,提出一种考虑数据采集算子形式的高效变量分裂方案,将数据采集算子根据欠采样掩码矩阵、傅里叶变换算子和线圈灵敏度矩阵进行拆分,简化算法子问题中二次项更新所涉及的矩阵逆运算,达到加快算法收敛速度的目的。仿真实验结果表明:与迭代软阈值法和共轭梯度法相比,所提算法在心电影数据集中收敛速度分别提高了57.9%和83.0%,结构相似性分别提升了3.3%和1.4%;在心脏灌注数据集中收敛速度分别提高了55.5%和79.6%,结构相似性分别提升了1.5%和0.4%。

Variable splitting algorithm is often used to solve the problem of under-sampled dynamic MRI(Magnetic Resonance Imaging) reconstruction by low rank and sparse matrix decomposition model. Aiming at the complex iterative calculation of conjugate gradient method in quadratic term updating, in order to speed up the reconstruction, this paper proposes an efficient variable splitting scheme considering the form of the data acquisition operator. The data acquisition operator is divided according to the under-sampled mask code matrix, the Fourier transform operator and the coil sensitivity matrix, which simplifies the matrix inverse operation involved in the update of the quadratic term in the algorithm subproblem, and achieves the purpose of accelerating the convergence speed the algorithm. Simulation results show that compared with the iterative soft threshold method and the conjugate gradient method, the convergence speed of the proposed algorithm in the cardiac cine dataset has increased by 57.9% and 83.0% respectively, and the structural similarity has increased by 3.3% and 1.4% respectively. In the cardiac perfusion dataset, the convergence speed has increased by 55.5%and 79.6% respectively, and the structural similarity has increased by 1.5% and 0.4% respectively.