Matrix Completion-Informed Deep Unfolded Equilibrium Models for Self-Supervised k-Space Interpolation in MRI

TL;DR

This paper introduces a self-supervised deep learning method for MRI k-space interpolation that leverages matrix completion theory and structural low-rankness, avoiding the need for fully sampled labels while ensuring convergence and high-quality reconstruction.

Contribution

It proposes a novel self-supervised deep equilibrium model for MRI that combines matrix completion with structural regularization, ensuring convergence without fully sampled labels.

Findings

Achieves MRI reconstruction performance comparable to supervised methods.

Outperforms existing self-supervised and traditional regularization approaches.

Ensures convergence through nonexpansive network structure.

Abstract

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.