Steve F,
What you really need is a raster to vector conversion. The raster image is composed of many pixels to make the illusion of vectored lines by one, having enough resolution so the mind will create the angles and polylines. Or two, using a technique of anti-roster that blends the edges of the small square to aid in the illusion. A vector image is a image of true lines, arcs, and polylines that are not composed of any square or pixels unless they are expressed in the file intentionally.
For anyone to use a low resolution bit map image (raster) and convert it a EPS (Embedded Post Script) or Adobe Illustrator file (both vector) would require a much higher resolution image and the conversion process in Illustrator with any good results. Or the artist would have to re-create the image from scratch and depending on the skill set of the individual, that would take several hours to say the lease...
Scott