Create Icons in Illustrator from JPG

I have a JPG file that is at too low a resolution to use. Current reolution is 100dpi. I need it recreated in Adobe Illustrator (required) so that it can be used for pre-press. We will need two colors - black and white. Not the whole design needs to be done, just the icons and numbers - the white items. The idea is that the white will be layer one, and then the black will be layered over the top. Although I guess I'm not being totally clear, the basic idea is that the icons and numbers need to be redone in Illustrator from scratch.