Physics-guided Self-supervised Implicit Neural Representation For Accelerated $\text{T}_{1\rho }$ Mapping

Quantitative $\text{T}_{1\rho }$ mapping has shown promise in clinical and research studies. However, it suffers from long scan times. Deep learning-based techniques have been successfully applied in accelerated quantitative MR parameter mapping. However, most methods require fully-sampled training dataset, which is impractical in the clinic. In this study, a novel scan-specific self-supervised method based on the implicit neural representation is proposed to reconstruct $\text{T}_{1\rho }$-weighted images and generate $\text{T}_{1\rho }$ map from highly undersampled $k$-space data, which only takes spatiotemporal coordinates as the input. Specifically, the proposed method learns an implicit neural representation of the MR images guided by the physical model of $\text{T}_{1\rho }$ mapping and two explicit priors: the signal relaxation prior and the self-consistency of $k$-t space data prior. The proposed method was verified using both retrospective and prospective undersampled $k$-space data. Experiment results demonstrate that it achieves a high acceleration factor up to 14, and outperforms the state-of-the-art methods in terms of suppressing artifacts and achieving the lowest error.