Weighted Nonlocal Total Variation in Image Processing

In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to balance between the labeled sets and unlabeled sets. With extensive numerical examples in semi-supervised clustering, image inpainting and image colorization, we demonstrate that WNTV provides an effective and efficient method in many image processing and machine learning problems.