Pixel adaptive deep-unfolding neural network with state space model for image deraining

Rain streaks affects the visual quality and interfere with high-level vision tasks on rainy days. Removing raindrops from captured rainy images becomes important in computer vision applications. Recently, deep-unfolding neural networks (DUNs) are shown their effectiveness on image deraining. Yet, there are two issues that need to be further addressed : 1) Deep unfolding networks typically use convolutional neural networks (CNNs), which lack the ability to perceive global structures, thereby limiting the applicability of the network model; 2) Their gradient descent modules usually rely on a scalar step size, which limits the adaptability of the method to different input images. To address the two issues, we proposes a new image de-raining method based on a pixel adaptive deep unfolding network with state space models. The proposed network mainly consists of both the adaptive pixel-wise gradient descent (APGD) module and the stage fusion proximal mapping (SFPM) module. APGD module overcomes scalar step size inflexibility by adaptively adjusting the gradient step size for each pixel based on the previous stage features. SFPM module adopts a dual-branch architecture combining CNNs with state space models (SSMs) to enhance the perception of both local and global structures. Compared to Transformer-based models, SSM enables efficient long-range dependency modeling with linear complexity. In addition, we introduce a stage feature fusion with the Fourier transform mechanism to reduce information loss during the unfolding process, ensuring key features are effectively propagated. Extensive experiments on multiple public datasets demonstrate that our method consistently outperforms state-of-the-art deraining methods in terms of quantitative metrics and visual quality. The source code is available at https://github.com/cassiopeia-yxx/PADUM.