  Diffusion-based inpainting can reconstruct missing image areas with high
quality from sparse data, provided that their location and their values are
well optimised. This is particularly useful for applications such as image
compression, where the original image is known. Selecting the known data
constitutes a challenging optimisation problem, that has so far been only
investigated with model-based approaches. So far, these methods require a
choice between either high quality or high speed since qualitatively convincing
algorithms rely on many time-consuming inpaintings. We propose the first neural
network architecture that allows fast optimisation of pixel positions and pixel
values for homogeneous diffusion inpainting. During training, we combine two
optimisation networks with a neural network-based surrogate solver for
diffusion inpainting. This novel concept allows us to perform backpropagation
based on inpainting results that approximate the solution of the inpainting
equation. Without the need for a single inpainting during test time, our deep
optimisation accelerates data selection by more than four orders of magnitude
compared to common model-based approaches. This provides real-time performance
with high quality results.
