Scott, I'm pretty sharp, but can't say I understand exactly what you're asking. Judging by the number of responses, I'm not alone in that..can you be a little more specific... Do you mean the ENTIRE image...or just the white portion? Do you want a crisp edged vector or the distressed "smeared" appearance like in the picture...?
Just the white portion of the graphic. I have tried applying a distressed filter to a clean vector but it doesn't look right. I would prefer the distressed appearance if that is possible.
If the image you've posted here is the same resolution as the one you are trying to use, you have a rough road ahead. The resolution is very low in the one I see...plus it's jpeg. Hi res Bitmap (bmp) or Portable Network Graphics (png) are your best file types for what you're working with. You will need the highest res you can find if the distressed look is your objective. From a vectorized POV that is probably not a goal you really want to pursue...especially if the final work is less than say 4 sqft in size and meant to be viewed up close, or for reprint. If ,on the other hand, it'll be large and viewed from a distance, detail won't be as crucial...Super hi res bitmap converted with one of the Quicktrace selections would be more than capable then...