Due to the negative ring around the center peak, this filter subtracts the background from the source in the middle. So this filter will remove background, which is only changing on large scales, from the image. That's what I meant with "background-free". It is effectively a band-pass filter which remove high spatial frequencies (smoothing) and low spatial frequencies (background subtraction). Does that make sense?

I think this filter is usefull for, e.g, source detection or multi-scale analysis...