  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 T1 and T1rho mapping sequence. The T1 and T1rho 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 T1 and T1rho parametric
maps close to the reference maps obtained by traditional mapping sequences,
even at a high acceleration rate of 14.
