# Convolutional Sparse Modular Fusion Algorithm for Non-Rigid Registration of Visible-Infrared Images
## 1 Introduction
With the advancement of deep learning technologies, learning-based registration methods have made significant progress. [PERSON] et al. [14] proposed a decoupled convolutional sparse coding model to uniformly handle both rigid and non-rigid registration, albeit with limited interference resistance; [PERSON] et al. [15] introduced ReCoNet, which can manage minor misalignments to a certain extent, while [PERSON] et al. [16] developed F3 Net, significantly improving remote sensing registration performance through frequency modulation. In the research of semantic-guided registration methods, [PERSON] et al. [17] proposed SuperFusion, which couples registration with semantic tasks yet faces speed bottlenecks; [PERSON] et al. [18] utilized a pre-trained segmentation network to extract foreground semantic positions, achieving fine cross-modal alignment. Although existing methods have made positive progress in various application scenarios, multimodal image registration still confronts numerous challenges: Firstly, the robustness of existing methods against complex environments and actual disturbances needs to be strengthened; Secondly, semantically guided methods commonly suffer from slow processing speeds and high task coupling degrees; Thirdly, designing more universal registration algorithms remains a significant challenge given the vast differencesbetween different modalities; Lastly, achieving real-time processing while maintaining high precision is still a considerable bottleneck in practical applications. This study proposes an Image Convolutional Sparse Fusion (ICSF) algorithm for visible-infrared image registration and fusion to address the abovementioned issues, offering a universal, lightweight, and modular framework. The ICSF framework comprises three main components: the feature decomposition network, the registration module, and the fusion module. The feature decomposition network enhances efficiency and accuracy by incorporating a self-attention mechanism into convolutional sparse coding, thereby separating homogeneous and isolated features. By extracting homogeneous features, multimodal image registration is simplified into single-modal registration, reducing computational complexity and improving accuracy. The fusion module processes feature groups to enhance the quality of the fused image. The key characteristics and contributions of ICSF are as follows:  
* To overcome the limitation of existing image fusion and registration methods, ICSF employs a modular design and several lightweight mechanisms. This design minimizes task coupling while ensuring the quality and speed of both image fusion and registration. In addition, ICSF is adaptable and can be deployed according to practical engineering requirements, making it suitable for a wide range of real-world applications. * An information entropy loss is introduced to guide feature extraction according to the expected objectives within the feature decomposition network. The registration module estimates parameters based on distinct homogeneous features while integrating a self-supervised registration loss informed by mutual information and a fully supervised prediction loss. In the fusion module, a fusion loss based on overall and gradient maximum correlation is introduced to preserve the scene content of the original image while enhancing textures in the fused image. * The ICSF algorithm has been tested across seven publicly available datasets, evaluating its functionality in terms of image registration accuracy, fusion performance, and speed, as well as extending to downstream tasks in image fusion. Both qualitative and quantitative experimental results validate the universality, effectiveness, and superiority of ICSF in terms of registration accuracy and fusion performance.