My iMac 27" Late 2012 has Image Persistence Problem

I'm wondering what to do about an annoying image persistence problem on my 27" late 2012 iMac. I got the iMac just a few days ago. Monday actually, so 4 days ago.

It's the 3.4GHz i7, 8GB, NVIDIA 680MX 1TB fusion drive model.

Overall it has become the love of my life, but the image persistence thing is getting harder to ignore. This happens after only a few minutes of use. If I follow Apple's instruction on dealing with LCD image persistence, I can make it go away for a while, but it comes back very quickly.

It is extremely noticeable on a plan dark background. It looks as thought he screen has been left on for a very long time with the same windows open, but it occurrs in less than 5 minutes of use with nothing more intense than a bit of web surfing.

I've read that this is happening a great deal on these new iMacs, particularly teh 27" machines.

While the problem seems to be known to those of us afflicted I don't know if Apple has acknowledged an issue or not.

Here is a sample of the complaints: http://forums.macrumors.com/showthread.php?t=1509571

I can make the ghost image vanish by bringing up an all white scree for a minute or so or using LCD Scrub.

I'm wondering if anyone else has foun a solution other than asking for a replacement computer, which Apple seems to be granting on this issue?