# Numerical computations of split Bregman method for fourth order total variation flow

## TL;DR

This paper develops numerical methods based on the split Bregman framework for fourth order total variation flow, including discretization techniques and a new shrinkage operator, with experiments demonstrating their effectiveness.

## Contribution

It introduces a novel numerical approach for fourth order total variation flow using split Bregman, including new discretization and shrinkage operators.

## Key findings

- Effective discretization of the problem using piecewise constant functions
- Development of a new shrinkage operator for Spohn's model
- Numerical experiments validate the proposed methods

## Abstract

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.