It depends on what background you mean.
If you mean that your application is running and you have some thread to get the image in the background thread, it is possible.
If you mean that your application is suspended and you still want to use PUSH notification and get the image. I am afraid that it is impossible. When your application is in the background, it has very limited amount of time that it can run to finish its current task. When that time is out, your application cannot do anything.
You can receive some push notification and local notification like GPS, server notification when your application is suspended, but you can only receive the server notification and cannot download the new image. Here is the instruction from Apple Dev documentation:
When the operating system delivers a
local or push notification and the
target application is not running in
the foreground, it presents the
notification (alert, icon badge
number, sound). If there is a
notification alert and the user taps
the action button (or moves the action
slider), the application launches and
calls the UIApplicationDelegate method
application:didFinishLaunchingWithOptions:,
passing in the local-notification
object or remote-notification payload.
If the application is running in the
foreground when the notification is
delivered, the
application:didReceiveRemoteNotification:
or
application:didReceiveLocalNotification:
method of the application delegate is
invoked.
More here