Replying to Photoshop help/ illustrator needed +k

Not sure if NSG is the best place to ask but i bet there is a lot of nser's who know a lot about illustrator and photo shop. I need to smooth out the edges on a couple pictures because when i imported them to illustrator then were all pixelated on the edges. I have to vectorize (confused about that) it and smooth the edges. if anyone could help me out i would really appreciate it. here are the pictures