Discrete zeroing neural dynamic with noise tolerance for image deblurring

As the demand for high-quality images continues to grow, image deblurring has become a fundamental challenge in computer vision. Although numerous effective deblurring methods have been proposed, one critical area remains largely unexplored: the interference caused by environmental noise. It is well known that noise can perturb solution systems, leading to instability or even collapse. Current mainstream methods, such as deep learning-based approaches, struggle to address such perturbations effectively. Additionally, these methods require large datasets for training and optimization, which incur significant computational cost and time. Without sufficient data, their robustness and deblurring performance are greatly limited. To address these challenges, we consider an alternative approach: a learning-free neural network, called neural dynamic. Our method employs a dynamic solving mechanism capable of addressing potential static optimization problems, while its integral term enhances noise resistance. To further adapt this framework for practical engineering applications, we developed a Taylor expansion-based discretization scheme called Taylor-type 6-instant Noise-Tolerance Zeroing neural Dynamic (T6NTZD). This model not only improves noise resistance but also achieves lightweight design and real-time processing. By introducing this approach, we aim to fill a significant gap in the field of image deblurring. Finally, through a detailed theoretical analysis from a continuous perspective and a comprehensive comparison with 12 neural dynamics models, the superiority of this method is clearly demonstrated. The key advantages of our model are summarized as follows: strong robustness, lightweight design, and the elimination of the need for data-intensive learning.