Explorations on anisotropic regularisation of dynamic inverse problems   by bilevel optimisation
  We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the application of video denoising. The optimisation poses a challenge in itself, as the dependency on one of the regularisation parameters is non-linear such that the standard existence and convergence theory does not apply. Moreover, we analyse numerical results of the proposed parameter learning strategy based on three exemplary video sequences and discuss the impact of these results on the actual modelling of dynamic inverse problems. 
Martin Benning and Carola-Bibiane Sch\"onlieb and Tuomo Valkonen and   Verner Vla\v{c}i\'c
math.NA