= Total variation calibration
For an <absolutely one-homogeneous functional> $J=\operatorname{TV}$ on a real <Hilbert space>, a <subgradient> $q$ at $u$ is characterized by $\langle q,v\rangle\le J(v)$ for every $v$ and $\langle q,u\rangle=J(u)$. A bounded <vector> field with $|z|\le1$ and $q=\operatorname{div}z$ proves the inequality through the dual definition, provided cutoff approximation is valid in the ambient space. Equality is called a calibration. It certifies a global minimizer of <total variation denoising>, rather than only a minimizer within a chosen ansatz.
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