  We present a parallel version of the cut-pursuit algorithm for minimizing
functionals involving the graph total variation. We show that the decomposition
of the iterate into constant connected components, which is at the center of
this method, allows for the seamless parallelization of the otherwise costly
graph-cut based refinement stage. We demonstrate experimentally the efficiency
of our method in a wide variety of settings, from simple denoising on huge
graphs to more complex inverse problems with nondifferentiable penalties. We
argue that our approach combines the efficiency of graph-cuts based optimizers
with the versatility and ease of parallelization of traditional proximal
