Unfolding High-order Correlations for Interpretable Multi-contrast MRI Super-resolution

Deep unfolding network has gained significant attention for magnetic resonance imaging super-resolution (MRI SR) due to its performance and interpretability. However, 1) existing methods predominantly focus on cross-contrast correlations while neglecting high-order correlations embedded within spatially adjacent slices in volumetric MRI data. 2) Their degradation models are optimized via the proximal gradient algorithm (PGA) that relies on manually designed hyperparameters (e.g., step size), often leading to overshooting or suboptimal solutions. To solve these limitations, we propose HocMRI, a deep unfolding multi-contrast MRI SR framework, which seamlessly integrates dual-prior modeling and hyperparameter-free PGA for enhanced reconstruction. Specifically, we first design a novel degradation model based on the dual-prior mechanism: an explicit prior based on low-rank tensor factorization to capture intra- and inter-slice dependencies, and an implicit prior leveraging a Mamba-based network with a novel 3D scanning strategy to further exploit high-order correlations across slices. Then, we derive a hyperparameter-free PGA to boost the traditional PGA, which employs a hyperbolic tangent function to dynamically control the gradient descent step, eliminating manual tuning while ensuring stable convergence with theoretical proofs. Based on the hyperparameter-free PGA, we develop an efficient iterative optimization algorithm to solve the degradation model and unfold it into a multi-stage deep network. Numerous experimental results from widely used MRI datasets demonstrate that our HocMRI achieves superior performance with enhanced efficiency compared to the state-of-the-art methods.