Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI
This addresses the challenge of practical MRI applications where fully sampled data is unavailable, offering a theoretically guaranteed self-supervised approach.
The authors tackled the problem of accelerated MRI reconstruction without fully sampled labels by proposing a self-supervised deep learning method that leverages matrix completion theory and low-rankness in k-space data, achieving performance comparable to supervised methods in some cases.
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.