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.

As a significant extension of classical clustering methods, ensemble clustering first generates multiple basic clusterings and then fuses them into one consensus partition by solving a problem concerning graph partition with respect to the co-association matrix. Although the collaborative cluster structure among basic clusterings can be well discovered by ensemble clustering, most advanced ensemble clustering utilizes the self-representation strategy with the constraint of low-rank to explore a shared consensus representation matrix in multiple views. However, they still encounter two challenges: (1) high computational cost caused by both the matrix inversion operation and singular value decomposition of large-scale square matrices; (2) less considerable attention on high-order correlation attributed to the pursue of the two-dimensional pair-wise relationship matrix. In this article, based on low-rank and sparse decomposition from both matrix and tensor perspectives, we propose two novel multi-view ensemble clustering methods, which tangibly decrease computational complexity. Specifically, our first method utilizes low-rank and sparse matrix decomposition to learn one common co-association matrix, while our last method constructs all co-association matrices into one third-order tensor to investigate the high-order correlation among multiple views by low-rank and sparse tensor decomposition. We adopt the alternating direction method of multipliers to solve two convex models by dividing them into several subproblems with closed-form solution. Experimental results on ten real-world datasets prove the effectiveness and efficiency of the proposed two multi-view ensemble clustering methods by comparing them with other advanced ensemble clustering methods.