  The split Bregman framework for Osher-Sol\'e-Vese (OSV) model and fourth
order total variation flow are studied. We discretize the problem by piecewise
constant function and compute $\nabla(-\Delta_{\mathrm{av}})^{-1}$
approximately and exactly. Furthermore, we provide a new shrinkage operator for
Spohn's fourth order model. Numerical experiments are demonstrated for fourth
order problems under periodic boundary condition.

Numerical Analysis;Numerical Analysis