Is it possible to get music from play;ist back into itunes library after computer factory reset

My computer had to be be factory reset after a big failure. now all my music is lost but my ipod has the music on it that i want to put back on to my computer. is there a way to movie it from the ipod back into the itunes library when they were NOT purchased from the itunes library?

if i want to add to my ipod at the moment, i have to erase everything on there as the itunes does not recognise it from the reset despite my account and computer being linked and authorised