Nonconvex models for recovering images corrupted by salt-and-pepper noise on surfaces

Image processing on surfaces has drawn significant interest in recent years, particularly in the context of denoising. Salt-and-pepper noise is a special type of noise which randomly sets a portion of the image pixels to the minimum or maximum intensity while keeping the others unaffected. In this paper, We propose the L$_p$TV models on triangle meshes to recover images corrupted by salt-and-pepper noise on surfaces. We establish a lower bound for data fitting term of the recovered image. Motivated by the lower bound property, we propose the corresponding algorithm based on the proximal linearization method with the support shrinking strategy. The global convergence of the proposed algorithm is demonstrated. Numerical examples are given to show good performance of the algorithm.