Zhongwei Shen

Carlos E. Kenig, Fanghua Lin, Zhongwei Shen

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_ε} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L_ε}. Most of our results, which rely on the recently established uniform estimates for the L^2 Dirichlet and Neumann problems in \cite{12,13}, are new even for smooth domains.

Congcong Bian, Haolong Ma, Hui Li et al.

Spatial registration across different visual modalities is a critical but formidable step in multi-modality image fusion for real-world perception. Although several methods are proposed to address this issue, the existing registration-based fusion methods typically require extensive pre-registration operations, limiting their efficiency. To overcome these limitations, a general cross-modality registration method guided by visual priors is proposed for infrared and visible image fusion task, termed FusionRegister. Firstly, FusionRegister achieves robustness by learning cross-modality misregistration representations rather than forcing alignment of all differences, ensuring stable outputs even under challenging input conditions. Moreover, FusionRegister demonstrates strong generality by operating directly on fused results, where misregistration is explicitly represented and effectively handled, enabling seamless integration with diverse fusion methods while preserving their intrinsic properties. In addition, its efficiency is further enhanced by serving the backbone fusion method as a natural visual prior provider, which guides the registration process to focus only on mismatch regions, thereby avoiding redundant operations. Extensive experiments on three datasets demonstrate that FusionRegister not only inherits the fusion quality of state-of-the-art methods, but also delivers superior detail alignment and robustness, making it highly suitable for infrared and visible image fusion method. The code will be available at https://github.com/bociic/FusionRegister.

Yuanchao Xu, Kaidi Shao, Nikos Logothetis et al.

Analyzing the long-term behavior of high-dimensional nonlinear dynamical systems remains a significant challenge. While the Koopman operator framework provides a powerful global linearization tool, current methods for approximating its spectral components often face theoretical limitations and depend on predefined dictionaries. Residual Dynamic Mode Decomposition (ResDMD) advanced the field by introducing the \emph{spectral residual} to assess Koopman operator approximation accuracy; however, its approach of only filtering precomputed spectra prevents the discovery of the operator's complete spectral information, a limitation known as the `spectral inclusion' problem. We introduce ResKoopNet (Residual-based Koopman-learning Network), a novel method that directly addresses this by explicitly minimizing the \emph{spectral residual} to compute Koopman eigenpairs. This enables the identification of a more precise and complete Koopman operator spectrum. Using neural networks, our approach provides theoretical guarantees while maintaining computational adaptability. Experiments on a variety of physical and biological systems show that ResKoopNet achieves more accurate spectral approximations than existing methods, particularly for high-dimensional systems and those with continuous spectra, which demonstrates its effectiveness as a tool for analyzing complex dynamical systems.

Hui Li, Haolong Ma, Chunyang Cheng et al.

For better explore the relations of inter-modal and inner-modal, even in deep learning fusion framework, the concept of decomposition plays a crucial role. However, the previous decomposition strategies (base \& detail or low-frequency \& high-frequency) are too rough to present the common features and the unique features of source modalities, which leads to a decline in the quality of the fused images. The existing strategies treat these relations as a binary system, which may not be suitable for the complex generation task (e.g. image fusion). To address this issue, a continuous decomposition-based fusion framework (Conti-Fuse) is proposed. Conti-Fuse treats the decomposition results as few samples along the feature variation trajectory of the source images, extending this concept to a more general state to achieve continuous decomposition. This novel continuous decomposition strategy enhances the representation of complementary information of inter-modal by increasing the number of decomposition samples, thus reducing the loss of critical information. To facilitate this process, the continuous decomposition module (CDM) is introduced to decompose the input into a series continuous components. The core module of CDM, State Transformer (ST), is utilized to efficiently capture the complementary information from source modalities. Furthermore, a novel decomposition loss function is also designed which ensures the smooth progression of the decomposition process while maintaining linear growth in time complexity with respect to the number of decomposition samples. Extensive experiments demonstrate that our proposed Conti-Fuse achieves superior performance compared to the state-of-the-art fusion methods.

Hui Li, Yongbiao Xiao, Chunyang Cheng et al.

Infrared and visible image fusion aims to generate synthetic images simultaneously containing salient features and rich texture details, which can be used to boost downstream tasks. However, existing fusion methods are suffering from the issues of texture loss and edge information deficiency, which result in suboptimal fusion results. Meanwhile, the straight-forward up-sampling operator can not well preserve the source information from multi-scale features. To address these issues, a novel fusion network based on the decomposition pooling (de-pooling) manner is proposed, termed as DePF. Specifically, a de-pooling based encoder is designed to extract multi-scale image and detail features of source images at the same time. In addition, the spatial attention model is used to aggregate these salient features. After that, the fused features will be reconstructed by the decoder, in which the up-sampling operator is replaced by the de-pooling reversed operation. Different from the common max-pooling technique, image features after the de-pooling layer can retain abundant details information, which is benefit to the fusion process. In this case, rich texture information and multi-scale information are maintained during the reconstruction phase. The experimental results demonstrate that the proposed method exhibits superior fusion performance over the state-of-the-arts on multiple image fusion benchmarks.