Yes, it’s possible, but there are no free methods that are easy. I’ve used an open source free software called PhotoRec in the past, but you have to be comfortable with using the command line and terminal in OS X.
One good, easy to use program is called CameraSalvage and it’s for OS X. It’s $50 to buy, but if you’ve got a card or a hard drive full of digital photos to rescue, that might be cheap.
All programs that rescue deleted files depend on the fact that computers and electronic devices like cameras, digital recorders (and many others) don’t fully erase files when a user deletes them. It’s a curious fact of computer technology and memory cards, but the reason they work that way is simple efficiency. It’s much simpler to delete the reference to a computer file or digital photo than go to the time and trouble of deleting the whole file.
If the pointer or catalog entry to a file is deleted, that’s just as good as deleting the whole file. But that’s where the unerase software comes in: it can go in and find files without needing the references and just look for the raw data and recover that.
If you formatted the card or completely erased it with the camera utility, you’re going to have a tougher time to recover photos, but some may still be fully recoverable.
And if you want to rescue files directly from a camera card, you’ll need a card reader for your Mac. If your photos are on a hard drive that crashed or you deleted the photos from it, you just need to be able to plug that hard drive into your Mac.
SubRosaSoft, the company that makes CameraSalvage has complete instructions on their website for using the program. I’ve run the trail version and it works well. Any photos you recover with the trail version will have “Demo” printed across them, but you can still use it to see how many pictures you can recover.