This paper proposes a second-order discrete total generalized variation (TGV) for arbitrary graphsignals, which we call the graph TGV (G-TGV). The original TGV was introduced as a natural higher-order extension of the well-known total variation (TV) and is an effective prior for piecewise smoothsignals.
Similarly, the proposed G-TGV is an extension of the TV for graph signals (G-TV) and inherits the capability of the TGV, such as avoiding staircasing effect. Thus the G-TGV is expected to be a fundamental building block for graph signal processing. We provide its applications to piecewise-smooth graph signal inpainting and 3D mesh smoothing with illustrative experimental results.