Parametric Maximum Flow Algorithms for Fast Total Variation Minimization

This report studies the global minimization of anisotropically discretized total variation (TV) energies with an Lᵖ (in particular, L¹ and L²) fidelity term using parametric maximum flow algorithms to minimize s-t cut representations of these energies. The TV/L² model, also known as the Rudin–Osher–Fatemi (ROF) model, is suitable for restoring images contaminated by Gaussian noise, while the TV/L¹ 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.