I'm not sure how important it is to be unbreakable, but a simple solution might just be to append a text file to the end of the image. Something like "This image belongs to ...".
If you open the image in a viewer/browser, it looks like a normal jpeg, but if you open it in a text editor, the last line would be readable.
The same method allows you include an actual file into an image. (hide a file inside of an image) I've found that it's a bit hit-or-miss, but 7-zip files seem to work. You could hide all sorts of copywrite goodies inside the image.
Again, it's not unbreakable by any stretch of the imagination, but it's completely invisible to the naked eye.
