In this work, we study a general framework of discrete approximations the total variation for image reconstruction problems. The framework, which can show consistency in sense $\Gamma$-convergence, unifies and extends several existing discretization schemes. addition, propose algorithms learning discretizations order to achieve best possible quality particular tasks. Interestingly, learned sign...

We consider whether minimizers for total variation regularization of linear inverse problems belong to $L^\infty$ even if the measured data does not. present a simple proof boundedness minimizer fixed parameter, and derive existence uniform bounds sufficiently small noise under source condition adequate priori parameter choices. To show that such result cannot be expected every fidelity term di...