How to turn a low pixel image into high pixel image?

Hi,

I have some images (logos) that I want to use for print on t-shirts.

The images I have are in rather low quality so the pixels are extremely visible when enlarged.

The images are mainly low in detail so its more a matter of getting the outlines smooth and in high resolution.

Below is one of the logos I want to use. I want to cut out the "impact" part, enlarge and prepare it for t-shirt  print.