VDMamba: Vector Decomposition in Vision Mamba for Image Deraining and Beyond

Image deraining aims to remove rain perturbations from rainy images and restore clear backgrounds. Recent research has employed the Mamba technique for image restoration, achieving exceptional results due to its effectiveness and efficiency in modeling long-range sequence relationships. However, a significant challenge remains: developing a comprehensive framework that considers the intrinsic coupling characteristics between image deraining and the Mamba architecture is largely unexplored. We propose that introducing a 1D sequential representation of Mamba could enhance image deraining by characterizing the direction-aware distribution of rain perturbations. This motivates us to introduce a new vector decomposition-based vision Mamba approach (VDMamba). This method investigates vector decomposition within the context of vision Mamba, addressing the challenging task of image deraining and beyond in the frequency embedding space. The key innovation of VDMamba is the Mamba-based vector decomposition and synthesis module (VDSM). This module derives 1D basic vectors (vertical and horizontal) from the frequency components via vector decomposition and employs the single-direction scanning of Mamba to eliminate the direction-specific degradation perturbation. This transformation allows the incipient Mamba to explore directionspecific global relationships for accurate perturbation learning, without requiring an elaborate design of the Mamba scanning. Additionally, the vertical and horizontal components in VDSM are encoded jointly in a bidirectional coupling manner, enabling the exploration of complementary and redundant components for refinement. Experiments on various image enhancement tasks, including image deraining, raindrop removal, rain haze removal, image dehazing, low-light image enhancement, and underwater image enhancement, demonstrate that VDMamba delivers competitive performance compared to the NeRD method. Specifically, it achieves a 0.58 dB improvement in PSNR for the image deraining task while reducing model parameters by 94.3%, computational cost by 88.3%, and inference time by 77.5%.