  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.
