4.2.1. Answer to how one can sharpen

Sharpen is in effect the reverse of blurring.
We sharpen by negating some of the energy of the surrounding pixels from the pixel at the processed position.

Demo

Open lena.png
Invoke the "Convolution Matrix" dialog.
Type 12 in the middle square and -1 in the 8 surrounding squares.
Type 4 as a divisor (12 + 8 * (-1) == 4).
Apply.