Theoretical guaranteed unfolding method for k-space interpolation in a self-supervised manner

Recently, iterative algorithm driven deep neural network unfolding methods have been successfully applied to MRI. However, the network replaces the original algorithm structure and mathematical properties such as interpretability and convergence of the original algorithm are not guaranteed. Fortunately, the k-space-filled Hankel low rank can naturally be associated with convolutional networks. Given this, we propose an unfolding method for k-space-filling, which guarantees convergence to the unique real MR image. Furthermore, we train this network in a self-supervised manner to cope with scenarios where fully sampled data are difficult to obtain. Finally, numerical experiments validate the effectiveness of the proposed method.