| Abstract: |
| Blind image deblurring is an inherently ill-posed problem, requiring the estimation of both blur kernel and the original image from a single blurred image. To achieve accurate estimation, prior knowledge is crucial. In this paper, we introduce the total curvature on image surface regularization prior, utilizing the image`s geometric features. This prior preserves sharp edges in the intermediate latent image and enhances the restoration of the blur kernel. We then propose a total curvature weighted image surface minimization model. The strong enhancement of edge preservation by total curvature allows for replacing $L_{0}$ norm with $L_p$ norm, ensuring sparsity in our model. This not only enhances our model`s performance but also improves its mathematical properties, enabling us to demonstrate its theoretical convergence. Furthermore, we incorporate inertial technology to enhance the numerical results of our algorithms. Extensive experiments demonstrate the superior performance of our method in diverse image deblurring scenarios compared to state-of-the-art methods. Notably, our method also extends its capabilities to non-uniform deblurring problems, showcasing its versatility and effectiveness in practical settings. |
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