Huber gradient regularizer

A Huber loss applied to a discrete gradient combines quadratic penalization of small slopes with linear penalization of large slopes. This interpolates between squared-gradient smoothing and total variation denoising, allowing smooth regions while retaining an edge-preserving large-gradient regime. The threshold should be chosen consistently with the signal's units and discretization. It can reduce staircasing in total variation denoising without guaranteeing its elimination.