If I understand correctly what they do now, they treat the diffraction pattern from X-rays going through a mask as a sort of 2-D Fourier transform, and transform it to an image with the inverse transform based on the known mask. Which is very clever. I don't doubt that this description glosses over the actually interesting bits.
[1] https://www.esa.int/ESA_Multimedia/Images/2019/02/Athena_mir...
[2] https://www.nasa.gov/feature/goddard/2019/nasa-s-new-lightwe...
The coded mask technology is really cool. The mask pattern is chosen in such a way that the inverse transform generates a unique solution (along with a whole lot of background noise that gets distributed more evenly and so can be subtracted out). Not to downplay that subtraction - modelling the noise in a coded mask system is one of the hardest parts of analysing the data. Worked on data from a coded mask mission once - 2 years to model the noise and correct for it, 6 months to do the science on the results.