Score-Based Diffusion Models With Self-Supervised Learning for Accelerated 3D Multi-Contrast Cardiac MR Imaging

Long scan time significantly hinders the widespread applications of three-dimensional multi-contrast cardiac magnetic resonance (3D-MC-CMR) imaging. This study aims to accelerate 3D-MC-CMR acquisition by a novel method based on score-based diffusion models with self-supervised learning. Specifically, we first establish a mapping between the undersampled k-space measurements and the MR images, utilizing a self-supervised Bayesian reconstruction network. Secondly, we develop a joint score-based diffusion model on 3D-MC-CMR images to capture their inherent distribution. The 3D-MC-CMR images are finally reconstructed using the conditioned Langenvin Markov chain Monte Carlo sampling. This approach enables accurate reconstruction without fully sampled training data. Its performance was tested on the dataset acquired by a 3D joint myocardial <inline-formula> <tex-math notation="LaTeX">$ \text {T}_{{1}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$ \text {T}_{{1}\rho }$ </tex-math></inline-formula> mapping sequence. The <inline-formula> <tex-math notation="LaTeX">$ \text {T}_{{1}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$ \text {T}_{{1}\rho }$ </tex-math></inline-formula> maps were estimated via a dictionary matching method from the reconstructed images. Experimental results show that the proposed method outperforms traditional compressed sensing and existing self-supervised deep learning MRI reconstruction methods. It also achieves high quality <inline-formula> <tex-math notation="LaTeX">$ \text {T}_{{1}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$ \text {T}_{{1}\rho }$ </tex-math></inline-formula> parametric maps close to the reference maps, even at a high acceleration rate of 14.