The jump penalty ‖ ‖ ∇ ∇ u ‖ ‖ 0 forces piecewise constant solutions and the data term ‖ ‖ u − − f ‖ ‖ p p couples the minimizing candidate u to the data f. The parameter γ > 0 controls the tradeoff between regularity and data fidelity. There are fast algorithms for the exact minimization of the L and the L -Potts functional.