  Harmonic inpainting with optimised data is very popular for inpainting-based
image compression. We improve this approach in three important aspects.
Firstly, we replace the standard finite differences discretisation by a finite
element method with triangle elements. This does not only speed up inpainting
and data selection, but even improves the reconstruction quality. Secondly, we
propose highly efficient algorithms for spatial and tonal data optimisation
that are several orders of magnitude faster than state-of-the-art methods. Last
but not least, we show that our algorithms also allow working with very large
images. This has previously been impractical due to the memory and runtime
requirements of prior algorithms.
