To do this I placed the image into Illustrator removing the background with the quick selection tool. Then saved it as a psd file so when you place it in Illustrator the background's gone, and it's as white as you see here.

 Then I rasterized it as you can see from the image on the right and changed the resolution to 20 instead of 300 which it is normally set to.

Rasterizing it pixelates on how much  depending on the resolution.