Estimating tissue parameter maps with high accuracy and precision from highly undersampled measurements presents one of the major challenges in MR fingerprinting (MRF). Many existing works project the recovered voxel fingerprints onto the Bloch manifold to improve reconstruction performance. However, little research focuses on exploiting the latent manifold structure priors among fingerprints. To fill this gap, we propose a novel MRF reconstruction framework based on manifold structured data priors. Since it is difficult to directly estimate the fingerprint manifold structure, we model the tissue parameters as points on a low-dimensional parameter manifold. We reveal that the fingerprint manifold shares the same intrinsic topology as the parameter manifold, although being embedded in different Euclidean spaces. To exploit the non-linear and non-local redundancies in MRF data, we divide the MRF data into spatial patches, and the similarity measurement among data patches can be accurately obtained using the Euclidean distance between the corresponding patches in the parameter manifold. The measured similarity is then used to construct the graph Laplacian operator, which represents the fingerprint manifold structure. Thus, the fingerprint manifold structure is introduced in the reconstruction framework by using the low-dimensional parameter manifold. Additionally, we incorporate the locally low-rank prior in the reconstruction framework to further utilize the local correlations within each patch for improved reconstruction performance. We also adopt a GPU-accelerated NUFFT library to accelerate reconstruction in non-Cartesian sampling scenarios. Experimental results demonstrate that our method can achieve significantly improved reconstruction performance with reduced computational time over the state-of-the-art methods.

翻译：从高度欠采样测量中高精度地估计组织参数图是磁共振指纹（MRF）的主要挑战之一。现有许多工作通过将恢复的体素指纹投影到布洛赫流形上以提升重建性能，但鲜有研究关注如何利用指纹间潜在的流形结构先验。为填补这一空白，我们提出一种基于流形结构化数据先验的新型MRF重建框架。由于直接估计指纹流形结构存在困难，我们将组织参数建模为低维参数流形上的点。研究揭示，尽管嵌入在不同欧氏空间中，指纹流形与参数流形共享相同的内在拓扑结构。为利用MRF数据中的非线性与非局部冗余性，我们将MRF数据划分为空间块，并通过参数流形中对应块之间的欧氏距离精确衡量数据块间的相似性。利用测得的相似性构建表征指纹流形结构的图拉普拉斯算子，从而借助低维参数流形将指纹流形结构引入重建框架。此外，我们在重建框架中融入局部低秩先验，进一步利用每个块内的局部相关性以提升重建性能。针对非笛卡尔采样场景，我们采用GPU加速的NUFFT库加速重建。实验结果表明，与最先进方法相比，本方法能在显著降低计算时间的同时实现大幅提升的重建性能。