Is it possible to have a picture instead of the current banner?
If you're using one of the standard themes then I'm afraid that you don't have full control of the banner.
The only theme that allows you to select your own banner image is Playtime. In this theme you can add an image to your assets library and select it as the banner by clicking on Options next to the theme on the Look & Feel page.
Your only other option currently, other than using Playtime, is to use the Custom theme and make something completely unique for your site - though this does require a knowledge of CSS.