Recover signal from its power spectral density
Generally (in the absence of prior knowledge) , I don't think this could be done. 

The PSD is the absolute value  squared of the DFT of the signal, and the abs function is not 1-to-1. For example abs(x) could be produced by f=x and f=-x. 

However, if you have some prior knowledge about the signal then you could reconstruct it from the PSD. Without more knowledge of what you're trying to do I don't think I could help you.