A good approximation of the original image from an observed image may be obtained by minimising a functional that consists of a data-fidelity term, a regularisation term, and a parameter, which balances data-fidelity and regularisation. Using the total variation as a regularisation term is a rather well understood concept of restoring images while preserving edges and discontinuities. If we have knowledge about the dynamic range in which the original image lies, then it seems natural to incorporate this information (via a box-constraint) into the model. Moreover, it is clear that the minimiser of the considered functional highly depends on the proper choice of the parameter.
In this talk we are wondering whether incorporating a box-constraint into the model really improves the quality of the solution or if it is indeed more a question of the proper choice of the regularisation parameter. Further we propose a semi-smooth Newton method for solving the considered models.