Quaternion Nuclear Norms Over Frobenius Norms Minimization for Robust Matrix Completion

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model multi-dimensional data, offer a promising framework for this problem. This paper introduces the quaternion nuclear norm over the Frobenius norm (QNOF) as a novel nonconvex approximation for the rank of quaternion matrices. QNOF is parameter-free and scale-invariant. Utilizing quaternion singular value decomposition, we prove that solving the QNOF can be simplified to solving the singular value $L_1/L_2$ problem. Additionally, we extend the QNOF to robust quaternion matrix completion, employing the alternating direction multiplier method to derive solutions that guarantee weak convergence under mild conditions. Extensive numerical experiments validate the proposed model's superiority, consistently outperforming state-of-the-art quaternion methods.

Task-Oriented Communications for Visual Navigation with Edge-Aerial Collaboration in Low Altitude Economy

To support the Low Altitude Economy (LAE), precise unmanned aerial vehicles (UAVs) localization in urban areas where global positioning system (GPS) signals are unavailable. Vision-based methods offer a viable alternative but face severe bandwidth, memory and processing constraints on lightweight UAVs. Inspired by mammalian spatial cognition, we propose a task-oriented communication framework, where UAVs equipped with multi-camera systems extract compact multi-view features and offload localization tasks to edge servers. We introduce the Orthogonally-constrained Variational Information Bottleneck encoder (O-VIB), which incorporates automatic relevance determination (ARD) to prune non-informative features while enforcing orthogonality to minimize redundancy. This enables efficient and accurate localization with minimal transmission cost. Extensive evaluation on a dedicated LAE UAV dataset shows that O-VIB achieves high-precision localization under stringent bandwidth budgets. Code and dataset will be made publicly available: github.com/fangzr/TOC-Edge-Aerial.

ePBR: Extended PBR Materials in Image Synthesis

Realistic indoor or outdoor image synthesis is a core challenge in computer vision and graphics. The learning-based approach is easy to use but lacks physical consistency, while traditional Physically Based Rendering (PBR) offers high realism but is computationally expensive. Intrinsic image representation offers a well-balanced trade-off, decomposing images into fundamental components (intrinsic channels) such as geometry, materials, and illumination for controllable synthesis. However, existing PBR materials struggle with complex surface models, particularly high-specular and transparent surfaces. In this work, we extend intrinsic image representations to incorporate both reflection and transmission properties, enabling the synthesis of transparent materials such as glass and windows. We propose an explicit intrinsic compositing framework that provides deterministic, interpretable image synthesis. With the Extended PBR (ePBR) Materials, we can effectively edit the materials with precise controls.

Interactive Gadolinium-Free MRI Synthesis: A Transformer with Localization Prompt Learning

Contrast-enhanced magnetic resonance imaging (CE-MRI) is crucial for tumor detection and diagnosis, but the use of gadolinium-based contrast agents (GBCAs) in clinical settings raises safety concerns due to potential health risks. To circumvent these issues while preserving diagnostic accuracy, we propose a novel Transformer with Localization Prompts (TLP) framework for synthesizing CE-MRI from non-contrast MR images. Our architecture introduces three key innovations: a hierarchical backbone that uses efficient Transformer to process multi-scale features; a multi-stage fusion system consisting of Local and Global Fusion modules that hierarchically integrate complementary information via spatial attention operations and cross-attention mechanisms, respectively; and a Fuzzy Prompt Generation (FPG) module that enhances the TLP model's generalization by emulating radiologists' manual annotation through stochastic feature perturbation. The framework uniquely enables interactive clinical integration by allowing radiologists to input diagnostic prompts during inference, synergizing artificial intelligence with medical expertise. This research establishes a new paradigm for contrast-free MRI synthesis while addressing critical clinical needs for safer diagnostic procedures. Codes are available at https://github.com/ChanghuiSu/TLP.

A New Adversarial Perspective for LiDAR-based 3D Object Detection

Autonomous vehicles (AVs) rely on LiDAR sensors for environmental perception and decision-making in driving scenarios. However, ensuring the safety and reliability of AVs in complex environments remains a pressing challenge. To address this issue, we introduce a real-world dataset (ROLiD) comprising LiDAR-scanned point clouds of two random objects: water mist and smoke. In this paper, we introduce a novel adversarial perspective by proposing an attack framework that utilizes water mist and smoke to simulate environmental interference. Specifically, we propose a point cloud sequence generation method using a motion and content decomposition generative adversarial network named PCS-GAN to simulate the distribution of random objects. Furthermore, leveraging the simulated LiDAR scanning characteristics implemented with Range Image, we examine the effects of introducing random object perturbations at various positions on the target vehicle. Extensive experiments demonstrate that adversarial perturbations based on random objects effectively deceive vehicle detection and reduce the recognition rate of 3D object detection models.

A Survey on Large Language Model-Based Social Agents in Game-Theoretic Scenarios

Game-theoretic scenarios have become pivotal in evaluating the social intelligence of Large Language Model (LLM)-based social agents. While numerous studies have explored these agents in such settings, there is a lack of a comprehensive survey summarizing the current progress. To address this gap, we systematically review existing research on LLM-based social agents within game-theoretic scenarios. Our survey organizes the findings into three core components: Game Framework, Social Agent, and Evaluation Protocol. The game framework encompasses diverse game scenarios, ranging from choice-focusing to communication-focusing games. The social agent part explores agents' preferences, beliefs, and reasoning abilities. The evaluation protocol covers both game-agnostic and game-specific metrics for assessing agent performance. By reflecting on the current research and identifying future research directions, this survey provides insights to advance the development and evaluation of social agents in game-theoretic scenarios.

DynamicAvatars: Accurate Dynamic Facial Avatars Reconstruction and Precise Editing with Diffusion Models

Generating and editing dynamic 3D head avatars are crucial tasks in virtual reality and film production. However, existing methods often suffer from facial distortions, inaccurate head movements, and limited fine-grained editing capabilities. To address these challenges, we present DynamicAvatars, a dynamic model that generates photorealistic, moving 3D head avatars from video clips and parameters associated with facial positions and expressions. Our approach enables precise editing through a novel prompt-based editing model, which integrates user-provided prompts with guiding parameters derived from large language models (LLMs). To achieve this, we propose a dual-tracking framework based on Gaussian Splatting and introduce a prompt preprocessing module to enhance editing stability. By incorporating a specialized GAN algorithm and connecting it to our control module, which generates precise guiding parameters from LLMs, we successfully address the limitations of existing methods. Additionally, we develop a dynamic editing strategy that selectively utilizes specific training datasets to improve the efficiency and adaptability of the model for dynamic editing tasks.

SCIGS: 3D Gaussians Splatting from a Snapshot Compressive Image

Snapshot Compressive Imaging (SCI) offers a possibility for capturing information in high-speed dynamic scenes, requiring efficient reconstruction method to recover scene information. Despite promising results, current deep learning-based and NeRF-based reconstruction methods face challenges: 1) deep learning-based reconstruction methods struggle to maintain 3D structural consistency within scenes, and 2) NeRF-based reconstruction methods still face limitations in handling dynamic scenes. To address these challenges, we propose SCIGS, a variant of 3DGS, and develop a primitive-level transformation network that utilizes camera pose stamps and Gaussian primitive coordinates as embedding vectors. This approach resolves the necessity of camera pose in vanilla 3DGS and enhances multi-view 3D structural consistency in dynamic scenes by utilizing transformed primitives. Additionally, a high-frequency filter is introduced to eliminate the artifacts generated during the transformation. The proposed SCIGS is the first to reconstruct a 3D explicit scene from a single compressed image, extending its application to dynamic 3D scenes. Experiments on both static and dynamic scenes demonstrate that SCIGS not only enhances SCI decoding but also outperforms current state-of-the-art methods in reconstructing dynamic 3D scenes from a single compressed image. The code will be made available upon publication.

GReDP: A More Robust Approach for Differential Privacy Training with Gradient-Preserving Noise Reduction

Deep learning models have been extensively adopted in various regions due to their ability to represent hierarchical features, which highly rely on the training set and procedures. Thus, protecting the training process and deep learning algorithms is paramount in privacy preservation. Although Differential Privacy (DP) as a powerful cryptographic primitive has achieved satisfying results in deep learning training, the existing schemes still fall short in preserving model utility, i.e., they either invoke a high noise scale or inevitably harm the original gradients. To address the above issues, in this paper, we present a more robust approach for DP training called GReDP. Specifically, we compute the model gradients in the frequency domain and adopt a new approach to reduce the noise level. Unlike the previous work, our GReDP only requires half of the noise scale compared to DPSGD [1] while keeping all the gradient information intact. We present a detailed analysis of our method both theoretically and empirically. The experimental results show that our GReDP works consistently better than the baselines on all models and training settings.

Quaternion Nuclear Norm minus Frobenius Norm Minimization for color image reconstruction

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.