The low-rank plus sparse (L+S) decomposition model has enabled better reconstruction of dynamic magnetic resonance imaging (dMRI) with separation into background (L) and dynamic (S) component. However, use of low-rank prior alone may not fully explain the slow variations or smoothness of the background part at the local scale. In this paper, we propose a smoothness-regularized L+S (SR-L+S) model for dMRI reconstruction from highly undersampled k-t-space data. We exploit joint low-rank and smooth priors on the background component of dMRI to better capture both its global and local temporal correlated structures. Extending the L+S formulation, the low-rank property is encoded by the nuclear norm, while the smoothness by a general \ell_{p}-norm penalty on the local differences of the columns of L. The additional smoothness regularizer can promote piecewise local consistency between neighboring frames. By smoothing out the noise and dynamic activities, it allows accurate recovery of the background part, and subsequently more robust dMRI reconstruction. Extensive experiments on multi-coil cardiac and synthetic data shows that the SR-L+S model outp

翻译：低秩加稀疏（L+S）分解模型通过将动态磁共振成像（dMRI）分离为背景（L）与动态（S）分量，已显著提升了其重建性能。然而，仅依赖低秩先验可能无法完全解释背景分量在局部尺度上的缓慢变化或平滑特性。本文提出一种平滑正则化L+S（SR-L+S）模型，用于高度欠采样k-t空间数据的dMRI重建。我们利用dMRI背景分量的联合低秩与平滑先验，以更好捕捉其全局与局部时间相关结构。该模型在L+S框架基础上，通过核范数编码低秩特性，并通过\ell_{p}范数正则项对L矩阵列向量的局部差异施加平滑约束。附加的平滑正则化可促进相邻帧间的分段局部一致性，通过抑制噪声与动态活动，实现背景分量的精确恢复，进而获得更鲁棒的dMRI重建。基于多线圈心脏数据与合成数据的广泛实验表明，SR-L+S模型优于传统方法。