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  1. Free, publicly-accessible full text available April 30, 2025
  2. Free, publicly-accessible full text available December 13, 2024
  3. Wang, L. (Ed.)
  4. Learned optimization algorithms are promising approaches to inverse problems by leveraging advanced numerical optimization schemes and deep neural network techniques in machine learning. In this paper, we propose a novel deep neural network architecture imitating an extra proximal gradient algorithm to solve a general class of inverse problems with a focus on applications in image reconstruction. The proposed network features learned regularization that incorporates adaptive sparsification mappings, robust shrinkage selections, and nonlocal operators to improve solution quality. Numerical results demonstrate the improved efficiency and accuracy of the proposed network over several state-of-the-art methods on a variety of test problems. 
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  5. This work aims at developing a generalizable Magnetic Resonance Imaging (MRI) reconstruction method in the meta-learning framework. Specifically, we develop a deep reconstruction network induced by a learnable optimization algorithm (LOA) to solve the nonconvex nonsmooth variational model of MRI image reconstruction. In this model, the nonconvex nonsmooth regularization term is parameterized as a structured deep network where the network parameters can be learned from data. We partition these network parameters into two parts: a task-invariant part for the common feature encoder component of the regularization, and a task-specific part to account for the variations in the heterogeneous training and testing data. We train the regularization parameters in a bilevel optimization framework which significantly improves the robustness of the training process and the generalization ability of the network. We conduct a series of numerical experiments using heterogeneous MRI data sets with various undersampling patterns, ratios, and acquisition settings. The experimental results show that our network yields greatly improved reconstruction quality over existing methods and can generalize well to new reconstruction problems whose undersampling patterns/trajectories are not present during training. 
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  6. Larochelle, H. ; Ranzato, M. ; Hadsell, R. ; Balcan, M. F. ; Lin, H. (Ed.)
    We propose a novel learning framework based on neural mean-field dynamics for inference and estimation problems of diffusion on networks. Our new framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities, which renders a delay differential equation with memory integral approximated by learnable time convolution operators, resulting in a highly structured and interpretable RNN. Directly using cascade data, our framework can jointly learn the structure of the diffusion network and the evolution of infection probabilities, which are cornerstone to important downstream applications such as influence maximization. Connections between parameter learning and optimal control are also established. Empirical study shows that our approach is versatile and robust to variations of the underlying diffusion network models, and significantly outperform existing approaches in accuracy and efficiency on both synthetic and real-world data. 
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