= Total variation denoising
{title2=$\min_u\{\operatorname{TV}(u)+\tfrac12\|u-g\|_2^2\}$}
For $g\in L^2$ on a bounded domain, total variation denoising has a unique minimizer. A bounded minimizing sequence has a weakly convergent $L^2$ subsequence; variation is a supremum of weakly continuous test-function pairings and the fidelity has <weak lower semicontinuity>. The <strictly convex> fidelity proves uniqueness. <Bounded-variation contraction under clipping> proves that data range bounds pass to the minimizer.
Back to article page
