Object controll with mouse position relative to circle

Object controll with mouse position relative to circle

Need some inspiration. I've got a picture (blue) and want it to move
proportional to the mouse position inside an invisible area (orange). So,
if the mouse moves in top-left direction, the image should follow the
movement.
I don't want to simply copy the mouse position, rather create an Joystick
like behaviour, so if the mouse moves, the image should move stepwise in
the desired direction.
But how? I've no idea how to set the right x+y coordinates for the image
or how to establish a formula to calculate them.