rough graph signals

Question

A common assumption in graph signal processing, especially when trying to derive geometric aspects based on the observed signals is that the values change smoothly across adjacent nodes. This then allows techniques like minimizing the total variation tr$(X^\top L X)$ in order to find the eigenvectors of an inferred graph laplacian matrix. For example https://arxiv.org/abs/1710.05654 Something I haven't been able to find is any reference or approach for when this assumption doesn't hold. Is there a graph signal model when the signals are rough? Thank you