Minimization of monotonically levelable higher order MRF energies via graph cuts
IEEE Transactions on Image Processing
Copula density estimation by total variation penalized likelihood with linear equality constraints
Computational Statistics & Data Analysis
Analysis and Generalizations of the Linearized Bregman Method
SIAM Journal on Imaging Sciences
Domain decomposition methods with graph cuts algorithms for total variation minimization
Advances in Computational Mathematics
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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.