In real-world time-series modelling, graph structures are widely adopted because they explicitly encode node topology and capture complex network dynamics. In practice, however, a complete graph is often partitioned across multiple parties; each party can access only its local sub-graph and, owing to privacy regulations, cannot share topology or data, creating pervasive data silos. Federated Graph Learning (FGL) offers a privacy-preserving collaborative-learning paradigm, yet current methods still face two key challenges: (1) the graph topology itself contains sensitive structural information, which can lead to privacy leakage if directly shared during FGL; (2) cross-party edges are crucial for accurate modeling, yet exploiting them without compromising privacy remains a significant challenge. To overcome these obstacles, we propose FedSkeleton, a privacy-preserving framework for time-series prediction that comprises a Skeleton Construction Module and a Dual-stream Forecasting Module, enabling global dependency capture without revealing the topology. Extensive experiments show that FedSkeleton consistently outperforms existing baselines and even surpasses models trained in a centralized setting with full-graph access in certain cases. In addition, we conduct comprehensive security analysis, communication-cost evaluation and scalability experiments, demonstrating that FedSkeleton effectively resists common attacks, keeps communication overhead manageable, and remains robust with respect to key hyper-parameters and the number of participating parties.

The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate of ADMM. However, determining optimal algorithmic parameters, including both the associated penalty and relaxation parameters, often relies on empirical approaches tailored to specific problem domains and contextual scenarios. Incorrect parameter selection can significantly hinder ADMM's convergence rate. To address this challenge, in this paper we first propose a general approach to optimize the value of penalty parameter, followed by a novel closed-form formula to compute the optimal relaxation parameter in the context of linear quadratic problems (LQPs). We then experimentally validate our parameter selection methods through random instantiations and diverse imaging applications, encompassing diffeomorphic image registration, image deblurring, and MRI reconstruction.

Abstract Image restoration with impulse noise is an important task in image processing. Taking into account the statistical distribution of impulse noise, the ℓ 1 ‐norm data fidelity and total variation () model has been widely used in this area. However, the model usually performs worse when the noise level is high. To overcome this drawback, several nonconvex models have been proposed. In this paper, an efficient iterative algorithm is proposed to solve nonconvex models arising in impulse noise. Compared to existing algorithms, the proposed algorithm is a completely explicit algorithm in which every subproblem has a closed‐form solution. The key idea is to transform the original nonconvex models into an equivalent constrained minimization problem with two separable objective functions, where one is differentiable but nonconvex. As a consequence, the proximal linearized alternating direction method of multipliers is employed to solve it. Extensive numerical experiments are presented to demonstrate the efficiency and effectiveness of the proposed algorithm.

The total variation infimal convolution (TV-IC) model combining Kullback–Leibler and ℓ2-norm data fidelity term works well for the inverse problem of mixed Poisson–Gaussian noise. Most existing algorithms for solving the TV-IC model rely on the Newton method to solve a nonlinear optimization subproblem, which inevitably increases the computation burden. In this study, we apply the first-order primal–dual Chambolle-Pock algorithm to solve the TV-IC model. In particular, we present an effective algorithm to solve the subproblem of the joint proximal operator with the Kullback–Leibler divergence and ℓ2-norm, which is based on the bilinear constraint alternating direction multiplier method. Numerical experiment results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for mixed Poisson–Gaussian denoising and deblurring problems.

Nowadays, motion attention model is a controversial topic in the biological computer vision area. The computational attention model can be decomposed into a set of features via predefined channels. Here we designed a bio-inspired vision attention model, and added the rarity measurement onto it. The priority of rarity is emphasized under the assumption of weighting effect upon the features logic fusion. At this stage, a final saliency map at each frame is adjusted by the spatiotemporal and rarity values. By doing this, the process of mimicking human vision attention becomes more realistic and logical to the real circumstance. The experiments are conducted on the benchmark dataset of static images and video sequences. We simulated the attention shift based on several dataset. Most importantly, our dynamic scenes are mostly selected from the objects moving on the highway and dynamic scenes. The former one can be developed on the detection of car collision and will be a useful tool for further application in robotics. We also conduct experiment on the other video clips to prove the rationality of rarity factor and feature cues fusion methods. Finally, the evaluation results indicate our visual attention model outperforms several state-of-the-art motion attention models.