# Dual-Branch CNN-Mamba Method for Image Defocus Deblurring
## 1 Introduction  
Defocus blurring is a common image distortion phenomenon that occurs when a camera or the human eye fails to focus accurately. Specifically, when the captured object is not aligned with the camera's focal point, the in-focus object appears sharp, while out-of-focus objects become blurred [1]. This blurring effect significantly degrades image quality and negatively impacts the subsequent tasks that rely on these images, such as image segmentation, object detection, and depth estimation. Therefore, researching effective methods for defocus deblurring is of considerable practical importance. As a fundamental research area in computer vision, image restoration encompasses tasks such as denoising, super-resolution, and deblurring. Among these, deblurring aims to recover sharp images from degraded observations, which is crucial for improvingthe quality of images in various applications, including medical imaging, autonomous driving, and photography. Defocus deblurring, as a specific type of deblurring, focuses on addressing the spatially varying blur caused by incorrect focal settings. Unlike motion blur or uniform blur, defocus blur exhibits unique characteristics, such as varying blur levels depending on the distance from the focal plane, making it a particularly challenging problem within the broader field of image restoration. Traditional defocus blur kernel estimation methods typically follow a two-stage approach. In the first stage, the blur kernel is obtained through blind estimation as proposed in [2; 3; 4], or by leveraging known prior information as described in [5; 6]. In the second stage, the blur kernel is used to recover the clear image through deconvolution or other inverse algorithms. While these methods rely on accurate blur kernel estimation, their effectiveness is limited, and their computational complexity is high, particularly when handling complex defocus blur. In recent years, deep learning-based approaches have improved the accuracy of blur kernel estimation as shown in [7; 8]. However, accurately estimating the blur kernel and using it for image recovery remains challenging. The complexity and diversity of defocus blur kernels have prompted researchers to explore non-kernel estimation approaches. In [9], an end-to-end convolutional neural network (CNN) is designed to directly learn the mapping between blurry and clear images using a large dataset of real defocus blur images, eliminating the need for kernel estimation. In [10], an iterative filtering adaptive network is employed to handle spatially varying and large defocus blur. In [11], a non-overlapping window self-attention mechanism is used to focus image features, enhancing detail recovery and demonstrating the remarkable potential of Transformer [12] in image restoration. The key feature of defocus blur is that the sharpness of the focal region and the blurriness of the foreground or background vary with distance. This spatially varying blur requires models to have strong local feature extraction capabilities to handle details under different blur levels, as well as global information modeling abilities to correctly process complex blur patterns. However, CNN-based deblurring methods are limited by the receptive field of the convolution kernels, making it difficult to capture sufficient global information. In contrast, Transformers excel at handling long-range dependencies and modeling complex blur patterns, but their local detail extraction capabilities are not as strong as those of CNNs. In addition, the quadratic complexity of the self-attention mechanism makes the computational complexity on high-resolution images very high. Although improvements to attention mechanisms have mitigated this to some extent, the demand for computational resources remains significant as the image resolution increases.