Thought this may be useful for you who are trying to remove artifacts when in fact, there's a real simple solution.

I know from my Photoshop experience that it works like a charm. You can try it with your Photoshop. Here's an actual example:

This is a cropped of an original JPEG file and it's compressed enough that you can see artifacts:

http://www.deafsuccess.com/jeff/P6290011.jpg

When you upsample that picture, you will see bigger artifacts:

http://www.deafsuccess.com/jeff/P6290011b.jpg

When you add noise (7.82% amount and distribution is Uniform in this case) to the image, the artifacts are dramatically lessened and the overall image quality improves:

http://www.deafsuccess.com/jeff/P6290011c.jpg

-jeff