There were some talks on the sparkfun forum about a driver board for the psp screen and I think someone made one. Can't remember the capabilities of it - not sure how easy it would be easy to use with an arduino.
Basically you can't use it with just an arduino but it would be possible with an additional driver board which does all the work.
An an example, even something like a 128x64 monochrome graphical display really needs to have a extra controller chip, typically the KS0108.
Mowcius