On the ROF Model in Rectilinear Anisotropy: Piecewise Constant Approximation and Universal Minimality

Abstract We prove that the $$L^2$$ L 2 distance between the minimizer of the $$\ell ^1$$ ℓ 1 -anisotropic Rudin-Osher-Fatemi (ROF) functional and its minimizer over the space of piecewise constant functions on a rectilinear grid is $$\mathcal {O}(h^{{1}/{2} - {q'}/{2q}})$$ O ( h 1 / 2 - q ′ / 2 q ) ... View More