Möbius Total Variation for Directed Acyclic Graphs

We propose a novel definition of total variation (TV) specifically defined for directed acyclic graphs (DAGs). It is a generalization of the classical definition for discrete-time signals (noting that discrete-time is a DAG) and obtained by inverting an integration operator on DAGs, leveraging the theory of Möbius inversion from combinatorics. We demonstrate the performance of our Möbius TV against prior TV definitions when used for denoising a set of real-world DAG signals.