Annihilation-Net: Learned annihilation relation for dynamic MR imaging.

Background: Deep learning methods driven by the low-rank regularization have achieved attractive performance in dynamic magnetic resonance (MR) imaging. The effectiveness of existing methods lies mainly in their ability to capture interframe relationships using network modules, which are lack interpretability.

Purpose: This study aims to design an interpretable methodology for modeling interframe relationships using convolutiona networks, namely Annihilation-Net and use it for accelerating dynamic MRI.

Methods: Based on the equivalence between Hankel matrix product and convolution, we utilize convolutional networks to learn the null space transform for characterizing low-rankness. We employ low-rankness to represent interframe correlations in dynamic MR imaging, while combining with sparse constraints in the compressed sensing framework. The corresponding optimization problem is solved in an iterative form with the semi-quadratic splitting method (HQS). The iterative steps are unrolled into a network, dubbed Annihilation-Net. All the regularization parameters and null space transforms are set as learnable in the Annihilation-Net.

Results: Experiments on the cardiac cine dataset show that the proposed model outperforms other competing methods both quantitatively and qualitatively. The training set and test set have 800 and 118 images, respectively.

Conclusions: The proposed Annihilation-Net improves the reconstruction quality of accelerated dynamic MRI with better interpretability.