# A Variational Neural Network Based on Algorithm Unfolding for Image Blind Deblurring  
[PERSON]  
1 College of Computer Science and Technology, Qingdao University, Qingdao 266071, China;  
1 [EMAIL_ADDRESS] (S.G.); [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (W.W.);  
1 [EMAIL_ADDRESS] (J.z)  
[PERSON]  
1 College of Computer Science and Technology, Qingdao University, Qingdao 266071, China;  
1 [EMAIL_ADDRESS] (S.G.); [EMAIL_ADDRESS] (Y.W. ); [EMAIL_ADDRESS] (W.W.);  
1 [EMAIL_ADDRESS] (J.z)  
[PERSON]  
2 School of Automation, Qingdao University, Qingdao 266071, China;  
2 [EMAIL_ADDRESS] 2 kpan@126. Ongoing research is necessary to refine the applicability of these models in practical image deblurring tasks. Building on these foundational insights, recent research has expanded the scope of image deblurring through advanced deep-learning architectures. The learning-based image deconvolutional network proposed by [PERSON] et al. [5] marks a critical advancement in this field. Various architectures for blind deblurring have emerged, notably those developed by [PERSON] et al. [6], [PERSON] et al. [7], and [PERSON] et al. [8]. Despite their promise, these methods face challenges due to the need for large amounts of training data, which can hinder generalization and model interpretability. To address the challenges associated with traditional image restoration methods, [PERSON] et al. [9] introduced the concept of algorithm unfolding, integrating variational models with deep learning techniques to enhance both the efficiency and interpretability of neural networks. This innovative approach initially found application in image compression perception [10] and has since been adapted across various domains [11; 12; 13], demonstrating its versatility in improving image quality. Subsequent advancements by [PERSON] et al. [14] involved integrating the unfolding of variational models into a neural network framework tailored for image blind deblurring. Nonetheless, this model exhibited limitations; discrepancies between estimated and actual blur kernels, along with inadequate utilization of image feature information, led to undesirable ghosting and ringing artifacts in the restored images. To mitigate these issues, researchers have been exploring more sophisticated network architectures and improved loss functions. For instance, adaptive reconstruction frameworks that dynamically adjust parameters based on the specific characteristics of images have shown promise in enhancing restoration quality. Furthermore, the incorporation of adversarial learning through generative adversarial networks (GANs) has proven effective in refining visual outcomes, allowing networks to better capture intricate details and structural nuances within images. However, the quest for robust solutions persists, particularly in addressing complex scenarios characterized by extreme blurriness. With the rapid development of deep learning technology, hybrid models have achieved remarkable results in many fields. For example, [PERSON] et al. [15] proposed a dynamic diffusion-variational neural network for spatio-temporal prediction, and [PERSON] et al. [16] proposed a variable-component convolutional neural network based on quantum filters and fully connected layers. Variational neural networks have been studied in various fields. In recent years, hybrid models combining deep learning and traditional regularization methods have become an important research direction in the field of deblurring. The regularization method is a technique used to prevent overfitting and improve the quality of image restoration by introducing prior knowledge or constraints. The core idea of regularization is to add an additional penalty term to the optimization problem, which limits the complexity of the model and helps it generalize better when faced with limited data. This approach not only reduces the risk of overfitting but also improves the smoothness, sharpness, and detail of the restored image.