http://www.jhendor.de/tutorials/cc2-ft.pdf describes how Ralf Schemann over at ProFantasy used a little toy I wrote a long time ago to do the sort of thing that you're asking. You would be particularly interested in the "Converting the image to an equirectangular projection" step, I'm guessing.
I haven't had a pressing need to use one of the projection tools out there, so I can't help you much with those, I'm afraid.
This image shows what the UI for ReprojectImage would look like to unproject a stereographic image
And this is a 4096x2048 export from those settings.
Other projections are pretty straightforward.
ReprojectImage is an ancient tool, but it sort of works for this kind of thing.



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