One can do a lot of things with Photoshop, but not miracles. If it is a low res photo and enlarging makes it unusable there are few easy ways to fix that.
Frequently it is best to find a better image, or build your own.
I have to agree with Curt Y- i think it may be best to just recreate the image out of vector. this was with vector you wont have to worry about if you need to further enlarge it, or printing clearly.
Curt Y's tutorial is almost spot on for what you want. If you have Illustrator, here is a useful tutorial: http://www.smashingmagazine.com/2010/11/15/illustrator-s-live-trace-sk etch-to-vector/
it might help you get familiar with vector for future projects.
I agree that re-drawing it is the best solution if possible, but if you end up with an image that you really, really need to preserve edges in when upsampling, there are a couple of specialty tools out there for doing just those kinds of operations...
I tried that totorial but couldn't get the lines perfectly even with each other which made the center look like a mess after it was twirled. Yours looks great and it looks better without the circle in the center. May I use it?