custom image for each category page

Hello,
I am working on a theme an have ran across a problem. I have a page that displays all of the children categories of its parent.

example category hierarchy
Mother
– son
– daughter
– ect.

When you select one of the child categories, the page reveals all the post listed within that child category. So for example,

– son <— category
— post about son <— post
— post about what son did. <— post

So within the “son” category, I want to have a custom image display on the page that shows all the post within that category and I would to have a different image for each category. Is this possible?

Thanks in advance.