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'Inferno' would be nice for this, also perceptually uniform, and has the benefit that space is still black.

Can you run it through the colormap in reverse to (approximately) recover the data?

Technically yes -- colormaps are 1-dimensional non-self intersecting curves in RGBA space. You just grab them by the... I mean just straighten them.

I don't know if an explicit formula for the colormap is given, but you can always do "xs = np.linspace(0,1,100); ys = { cm.hot(x):x for x in xs}" and recover an approximate inverse. Then apply this function to each pixel of the image.

Based on my analysis the published image is too processed to be able to invert the colormap to get to the brightness temperature data. I had better luck with Paper IV Fig. 15. See: https://physics.stackexchange.com/questions/472641/what-woul...

You can easily remap it between different colour maps if you assume that is is a standard hot map.