Many Windows programs will run under WINE (which means "Wine Is Not an Emulator). You can learn more about WINE and find out what programs have been tested (along with those results) at http://www.winehq.org/
I took a look and it appears that some versions of PS Elements work better than others, so you'd just have to give it a try.
WINE is not installed by default in Mint IIRC, but it's easy to get. In the Mint menu, click the Package Manager, enter your root password, and type "wine" in the search window. Then you can install it from there.
Hope this helps.
You don't have a soul. You are a Soul. You have a body. - C. S. Lewis