Non-Lipschitz Variational Models and their Iteratively Reweighted Least Squares Algorithms for Image Denoising on Surfaces

SIAM Journal on Imaging Sciences, Volume 17, Issue 2, Page 1255-1283, June 2024.
Abstract.Image processing on surfaces has gotten increasing interest in recent years, and denoising is a basic problem in image processing. In this paper, we extend non-Lipschitz variational methods for 2D image denoising, including TV[math], to image denoising on surfaces. We establish a lower bound for nonzero gradients of the recovered image, implying the advantage of the models in recovering piecewise constant images. A new iteratively reweighted least squares algorithm with the thresholding and support shrinking strategy is proposed. The global convergence of the algorithm is established under the assumption that the object function is a Kurdyka–Łojasiewicz function. Numerical examples are given to show good performance of the algorithm.