Adaptive geometric joint prior image deblurring model based on multi-regularization

Curvature regularization has become a fundamental tool in image processing due to its strong priors for edge preservation. In this paper, we introduce a novel multi-regularization framework that incorporates Gaussian curvature, mean curvature and surface area, enabling adaptive selection of geometric priors in different regions based on their specific characteristics. To efficiently optimize this term, we utilize a curvature filter that implicitly enforces curvature constraints without the need for explicit calculations, significantly enhancing computational efficiency. Additionally, we incorporate gradient $L_p$ norm constraint, which not only preserve image edges more effectively but also can promote the sparseness of the model. Our approach is further supported by an ADMM-based optimization algorithm tailored to solve the model. Extensive comparison experiments demonstrate the effectiveness, robustness, and superiority of the proposed regularization framework for image deblurring tasks.