A comparison of three total variation based texture extraction models

This paper qualitatively compares three recently proposed models for signal/image texture extraction based on total variation minimization: the Meyer [27], Vese-Osher (VO) [35], and TV-L1 [12,38,2–4,29–31] models. We formulate discrete versions of these models as second-order cone programs (SOCPs) which can be solved efficiently by interior-point methods. Our experiments with these models on 1D oscillating signals and 2D images reveal their differences: the Meyer model tends to extract oscillation patterns in the input, the TV-L1 model performs a strict multiscale decomposition, and the Vese-Osher model has properties falling in between the other two models.