  Recently, regularization model-driven deep learning (DL) has gained
significant attention due to its ability to leverage the potent
representational capabilities of DL while retaining the theoretical guarantees
of regularization models. However, most of these methods are tailored for
supervised learning scenarios that necessitate fully sampled labels, which can
pose challenges in practical MRI applications. To tackle this challenge, we
propose a self-supervised DL approach for accelerated MRI that is theoretically
guaranteed and does not rely on fully sampled labels. Specifically, we achieve
neural network structure regularization by exploiting the inherent structural
low-rankness of the $k$-space data. Simultaneously, we constrain the network
structure to resemble a nonexpansive mapping, ensuring the network's
convergence to a fixed point. Thanks to this well-defined network structure,
this fixed point can completely reconstruct the missing $k$-space data based on
matrix completion theory, even in situations where full-sampled labels are
unavailable. Experiments validate the effectiveness of our proposed method and
demonstrate its superiority over existing self-supervised approaches and
traditional regularization methods, achieving performance comparable to that of
supervised learning methods in certain scenarios.
