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Exploiting Manifold Structured Data Priors for Improved MR Fingerprinting Reconstruction

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.

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