this isn't PS2/PS1/etc, but with a PSP+Linux, you can make a backup by doing the following:
(as root)
# mkdir /mnt/psp
# mount /dev/node/of/psp/heer /mnt/psp
(as regular user)
$ dd if="/dev/node/of/psp/heer" of "~/psp.img"
$ chmod 644 psp.img
(and to read/write to your PSP memstick image, if needed, within Linux, do the following (make sure the loopback device is in your kernel, also needs root access)):
# mount -o /path/to/your/home/directory/heer/psp.img /mnt/psp
then you can do whatever you want. (if I messed any of this up, feel free to correct me :)
(you should have the amount of free space needed as per your memory stick though. example: you have a 1GB stick, you'll need 1GB free.)
also, if there's a card reader/writer which reads PS1/PS2/GC/etc memory cards, and it works in Linux, you could probably do this too.