Another opportunity for efficient blur would be to rescale the image if the blur radius is above a certain amount. This incurs overhead, so for smaller radii it might be more efficient to just blur the full-size image, but for larger radii you can first reduce the image, blur with a smaller radius, and then upscale the image.

You might need an Arbitrary Hack Constant (oh, sorry, "tuning parameter") to decide when to make that transition.