For a quick & dirty solution, I would create HTML widget and insert into Global header.
In Appearance -> Custom Javascript, I would add the magic here.
You can upload the images into Public folder and then create an array in the javascript.
You can grab the title via the <meta name="title" content="Cat title"> tag and match it up with the images array. This is very manual so every time you change the category name you'll have to change in the javascript code as well. I take it though category name won't change that much when Live.
I have not tried this yet as It's just in theory.
