Projection residual for discrete total variation
= Projection residual for discrete total variation
{title2=$u=g-P_Cg$}
For $C=D^*\{p:|p_i|_2\le\lambda\}$, discrete <total variation denoising> is the <proximal operator> of the <support function> of $C$. The <Moreau decomposition> gives the displayed projection residual. It is generally not itself a <metric projection onto a closed convex set>: such a projection is idempotent, but TV denoising shrinks a sufficiently large two-level jump again when reapplied.