2. Optimizing spatial and tonal data for PDE-based inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in themissing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimizing this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work.