Parametric Maximum Flow Algorithms for Fast Total Variation Minimization

Abstract

This report studies the global minimization of anisotropically discretized total variation (TV) energies with an $L^p$ (in particular, $L^1$ and $L^2$) fidelity term using parametric maximum flow algorithms to minimize $s$-$t$ cut representations of these energies. The TV/$L^2$ model, also known as the Rudin-Osher-Fatemi (ROF) model, is suitable for restoring images contaminated by Gaussian noise, while the TV/$L^1$ model is able to remove impulsive noise from grayscale images and perform multiscale decompositions of them. Preliminary numerical results on large-scale two-dimensional CT and three-dimensional brain MR images are presented to illustrate the effectiveness of these approaches.