Mattias Samland (MPIA), as part of his PhD dissertation, adapted the CPM model we built to calibrate (and image-difference) Kepler and TESS imaging to operate on direct imaging of exoplanets. The idea is that the direct imaging is taken over time, and speckles move around. They move around continuously and coherently, so a data-driven model can capture them, and distinguish them from a planet signal. (The word "causal" is the C in CPM, because it is about the differences between how systematics and real signals present themselves in the data.) There is lots of work in this area (including my own), but it tends to make use of the spatial (and wavelength) rather than temporal coherence. The CPM is all about time. It turns out this works extremely well; Samland's adaptation of CPM looks like it outperforms spatial methods, especially at small “working angles” (near the nulled star; this is coronography!).
But of course a model that uses the temporal coherence but ignores the spatial and wavelength coherence of the speckles cannot be the best model! There is coherence in all four directions (time, two angles, and wavelength) and so a really good speckle model must be possible. That's a great thing to work on in the next few years, especially with the growing importance of coronographs at ground-based and space-based observatories, now and in the future. Samland and I discussed all this, and specifics of the paper he is nearly ready to submit.
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