Local Curvature Optimization for Self-Supervised Image Restoration

This letter introduces an innovative approach for image restoration. Our model is primarily motivated by the integration of curvature constraints into a self-supervised convolutional neural network (CNN), which combine the hand-crafted prior with CNN structure without training on external dataset. Firstly, it is argued that detail loss may be induced by sparsity-based models, which eliminate bases with low coefficients. Therefore, a geometric approach is proposed to preserve details, with the incorporation of Gaussian curvature as a regularization term for both noise suppression and detail preservation. Secondly, the deep image prior is used to establish the optimization backbone. This framework harnesses the translation in-variance and smoothness properties of CNN as a tightly supervised recovery mechanism for effective noise suppression. By combining a simple data-fitting term with curvature-based regularization terms, we develop a self-supervised model for image restoration that maintains fine details. Experimental results demonstrate the effectiveness of our proposed algorithm in addressing various image restoration problems.