  Inpainting-based compression represents images in terms of a sparse subset of
its pixel data. Storing the carefully optimised positions of known data creates
a lossless compression problem on sparse and often scattered binary images.
This central issue is crucial for the performance of such codecs. Since it has
only received little attention in the literature, we conduct the first
systematic investigation of this problem so far. To this end, we first review
and compare a wide range of existing methods from image compression and general
purpose coding in terms of their coding efficiency and runtime. Afterwards, an
ablation study enables us to identify and isolate the most useful components of
existing methods. With context mixing, we combine those ingredients into new
codecs that offer either better compression ratios or a more favourable
trade-off between speed and performance.
