I need two images to be re-formatted so that they can be enlarged without pixelating.

Design details: I have two images that need to be re-formatted so that when enlarged they don't pixelate. The two images are of a cartoon man. It may be that the original format is changed to a vector or pdf or something similar. The images are to be used on large format signs and for use in marketing material. The images themselves can not be altered as they are the existing logos.
Ideas for the visual style: No change to the existing images, just the ability to enlarge the image successfully.
Extra notes: