中文摘要：

本文提出一种基于多尺度低秩模型（MSL,Multi-Scale Low rank）的磁共振成像方法,该方法将矩阵分解成多尺度的块低秩矩阵之和,并将多尺度块低秩矩阵之和的最小化作为约束条件用于磁共振成像.两种不同的心脏磁共振数据用于验证本文所提出算法重构磁共振成像的精度.实验结果表明,相比于k-t SLR（k-t Sparsity Low Rank）和L＋S（Low Rank plus Sparse）方法,所提出的MSL方法具有更好的重建效果,获得更高的重构信差比（signal to error ratio）,并具有更好地结构相似性,但需要更长的重构时间.

英文摘要：

This paper presents a multi-scale low rank based method to implement cardiac MR（ Magnetic Resonance） image reconstruction,which represented a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. And the sum of block-wise low rank matrices was used as a constraint to approach the MR image reconstruc- tion. Two different cardiac MR datasets were used to evaluate the performance of the proposed method. Compared with the state-of-art methods,such as the k-t SLR（k-t Sparsity Low Rank） method and L ＋ S （Low rank plus Sparse） method,the proposed MSL method can offer improved reconstruction solution in terms of higher signal to error ratio and better structural similarity index, but with longer reconstruction time.