Some unsharp algorithms (e.g. Matlab's fspecial) use a Laplacian kernel to achieve sharpening of the image.
From what I know, the image needs to be blurred first, and then the blurred image is subtracted from the original to get a sharper image. The Laplacian part comes exactly where alleged smoothing should take place. Correct me if I'm wrong, but Laplacian doesn't do any smoothing.
So how does the Laplacian help in sharpening the image?