Learning Consistent Discretizations of the Total Variation

In this work, we study a general framework of discrete approximations of the total variation for image reconstruction problems. The framework, for which we can show consistency in the sense of Γ-convergence, unifies and extends several existing discretization schemes. In addition, we propose algorithms for learning discretizations of the total variation in order to achieve the best possible reconstruction quality for particular image reconstruction tasks. Interestingly, the learned discretizations significantly differ between the tasks, illustrating that there is no universal best discretization of the total variation.