Graph total variation denoising ($\hat{\theta }=\arg {\min }_{\theta }\{n^{-1}\Vert y-\theta {\Vert }_2^2+\lambda \Vert D\theta {\Vert }_1\}$)

Graph total variation denoising is a penalized least-squares estimator for noisy vertex signals on a graph. The squared loss is strictly convex, so the fitted signal is unique. Its basic inequality for a penalized least-squares estimator separates a noise inner product from the change in penalty. The incidence pseudoinverse decomposition controls the nonconstant noise through the geometry of the graph.