Box-constrained TV-L1 denoising (${\min }_{0\le u\le 1}\Vert u-f{\Vert }_1+\lambda {\mathrm{TV}}_{\mathrm{iso}}(u)$)

This finite-image convex optimization model combines robust L1 norm fidelity with discrete isotropic total variation and pixel-range constraints. An exact second-order cone program uses two orthant fidelity slacks per pixel, two box slacks per pixel and a three-dimensional Lorentz cone for each gradient magnitude. The product canonical barrier has parameter $6n$ for $n$ pixels.