Total-Variation Mode Decomposition

Ido Cohen et al. code

In this work we analyze theTotal Variation(TV) flow ap-plied to one dimensional signals. We formulate a relation between Dynamic Mode Decomposition(DMD), a dimensionality reduction method basedon the Koopman operator, and the spectral TV decomposition. DMD isadapted by time rescaling to fit linearly decaying processes, such as theTV flow. For the flow with finite subgradient transitions, a closed formsolution of the rescaled DMD is formulated. In addition, a solution to theTV-flow is presented, which relies only on the initial condition and itscorresponding subgradient. A very fast numerical algorithm is obtainedwhich solves the entire flow by elementary subgradient updates.