I think JavaLawyer is the best one to help with this, but I will take a stab at it. First check Account Management > Network Shares options and see if you have the Recycle Bin and if you do, that will show you where your pictures are.
If not..then things get alot more complicated. The main problem is your computer didn't delete the files, it told another copmputer (your DNS-320) to delete them. I think the DNS-320 uses EXT3, so if you removed the drive, put it into a linux system and used some data recovery software, it "might" work. I say might because EXT3 is set up for reasons of stability, EXT3 0's out the block pointers.
Another way to go, is check to see if maybe your Picaso is backed up in the cloud? Do you have Dropbox linked to your account? Or maybe backup to Google Drive?