 Discrete Hessian-norm denoising

Replacing a discrete gradient by a second-difference operator $H:X\to X^4$ gives the global-norm penalty $\alpha \Vert Hu{\Vert }_2$. Its reconstruction is $g-P_{C}g$ for $C=H^{\ast }{B}_{\alpha }$. Components in $\ker H$ are preserved; affine-image membership of this kernel depends on the boundary stencil. Pixelwise Hessian penalties instead use a product of four-component balls.