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Purpose  Magnetic resonance fingerprinting (MRF) methods typically rely on dictionary matching to map the temporal MRF signals to quantitative tissue parameters. Such approaches suffer from inherent discretization errors, as well as high computational complexity as the dictionary size grows. To alleviate these issues, we propose a HYbrid Deep magnetic ResonAnce fingerprinting (HYDRA) approach, referred to as HYDRA.    Methods  HYDRA involves two stages: a model‐based signature restoration phase and a learning‐based parameter restoration phase. Signal restoration is implemented using low‐rank based de‐aliasing techniques while parameter restoration is performed using a deep nonlocal residual convolutional neural network. The designed network is trained on synthesized MRF data simulated with the Bloch equations and fast imaging with steady‐state precession (FISP) sequences. In test mode, it takes a temporal MRF signal as input and produces the corresponding tissue parameters.    Results  We validated our approach on both synthetic data and anatomical data generated from a healthy subject. The results demonstrate that, in contrast to conventional dictionary matching‐based MRF techniques, our approach significantly improves inference speed by eliminating the time‐consuming dictionary matching operation, and alleviates discretization errors by outputting continuous‐valued parameters. We further avoid the need to store a large dictionary, thus reducing memory requirements.    Conclusions  Our approach demonstrates advantages in terms of inference speed, accuracy, and storage requirements over competing MRF methods.

HYDRA: Hybrid deep magnetic resonance fingerprinting