Usually when we use 'pick up' in this way, it means we are learning something for the first time. If we learn something, then forget it, and are learning it again, we should use 'again' with 'pick up' to point this out.To pick up something can be equivalent to to learn something. Let's say we have learned how to solve a math problem in the past, yet we forget how to do it. If that math problem is not hard to solve once we try to do some similar problems, can we still say that it's not hard to PICK UP that math problem once we start to do some similar problems even though we have already learned how to solve it in the past?
Ex. I forgot all the trigonometric identities I learned in high school, but picked them up again in college.
Ex. I forgot how to use the Chain Rule until I worked some example problems and picked it up again.
If you are learning something that is similar or related to what you learned before, but is not exactly the same, you can use 'pick up'.
Ex. I picked up my algebra really well in high school, so all the algebraic manipulation I had to do for Calculus was easy to pick up too.
Normally though, 'relearn' is used to show something is being learned again.