I think it's important to be aware that your permission to post the image is largely unconnected with how you attribute the image.
You're dealing with a visual work that is presumably protected by copyright. If that's the case, the author has the exclusive right to publicly display the work, which means you do not have the right to publicly display the work (by posting it online, for instance).
If you knew who the artist was, you might be able to obtain a license from her that would allow you to post it online. The odds are good that that license would require you to attribute it to the artist, but failing to do so would probably just be a violation of your contract, not of copyright law.
But since you can't obtain a license, you have to ask whether there's some exception that would permit you to use it without the author's permission.
The go-to is usually fair use, but we don't have enough information to indicate whether this hypothetical would give rise to a fair use. To do so, we'd need to know more about:
- the purpose of displaying it on your website;
- the kind of image you want to copy;
- how much of it you want to use; and
- how your use might effect the commercial market for the image.
There are other possibilities, as well, but none that seem particularly useful. For instance, there's the first-sale doctrine, which allows someone who legally obtains a work to publicly display it, but that wouldn't help you because it's limited to displays "at the place where the copy is located." A court would treat the image as being located on a server, not online, so publishing it to your site would not be permissible.
(All this assumes that you're publishing from the United States. Copyright rules are different from jurisdiction to jurisdiction.)