depending on just what input data you have
MMPS is not bad

the main issues are the correct mapping at and near the poles

gimp has a built in tool to remap to polar projection

this in combination with the gimp plugin "Resynthesizer"

http://www.logarithmic.net/pfh/resynthesizer

the source code
https://github.com/bootchk/resynthesizer

you can then "fix" the area at the poles

or
use the built in tool "heal" to fix small areas