Repairing Cat Claw Punctures in Faux Leather Furniture?

I have a beautiful sofa and chair with faux leather arms and backs. The cat has made small punctures in the arms. They aren't bad, but you can feel them when you run your hand over the arm. Is there a way to get rid of them or make them less noticeable? The furniture is only 2 years old, I can't afford to get new.