For this first of all you need to set a tag for your ImageView
<ImageView
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:id="@+id/imageview1"
android:background="@drawable/bg1"
android:tag="bg1"/>
Now get the image name currently set on your ImageView by doing the following,
ImageView v = (ImageView)findViewbyId(R.id.img);
String backgroundImageName = String.valueOf(v.getTag());
and this should return the image tag name which is "bg1".
Now compare the tag names or use it for further process
if( backgroundImageName.equals(bg1))
{
//do something
}
else{
//do something
}