Go to apps and look for "My Gallery". tap on it then tap the menu button on the bottom left and choose settings. In the settings menu uncheck "display friends activities". That setting, when checked downloads pictures from facebook and if you have friends that like to upload a lot of pictures, it will be constantly downloading them to your gallery.
Also, in the screenshot you posted above, you can click on the "media" icon and then tap on "force close" to shut it down. Chances are though it will reactivate.
Other things that may be using that app are music streaming apps.
Just some thoughts.