Matrix representation of a linear transformation using the elementary basis of $\mathbb{R}^{M\times N}$. Compact representation of $w(s,t)$.
Box filter as an example. $TV(w * g)\le TV(g)$.
Edge detection
$$
g(x,y)=f(x,y)+c \Delta f(x,y) \, ,
$$
with $c<0$.
Reading materials
Lecture Notes: p.45-49.
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