HG-MRF: Anatomy-Aware Hierarchical Hypergraph Regularization for MR Fingerprinting Reconstruction

We introduce a novel hierarchical hypergraph model (HGMRF) for improved MRF reconstruction. HG-MRF constructs a K-uniform hypergraph in which each voxel is a vertex, and hyperedges connect multiple voxels to capture higher-order, spatially distant, and structurally related dependencies. To ensure anatomical consistency without incurring prohibitive computational cost, we introduce a hierarchical construction strategy with three stages: anatomy-aware vertex clustering based on tissue similarity, intra-hyperedges construction among closely related vertices within each cluster, and inter-hyperedge establishing to encode broader contextual dependencies across clusters. The resulting hypergraph is then integrated into the reconstruction model via a Laplacian eigenmaps-based regularization term, serving as a powerful, anatomy-aware prior that promotes consistent parameter estimation across structurally related voxels. Experiments show that HG-MRF outperforms state-of-the-art methods, with improved reconstruction quality and computational efficiency.