  We present a novel approach to denoising and inpainting problems for surface
meshes. The purpose of these problems is to remove noise or fill in missing
parts while preserving important features such as sharp edges. A discrete
variant of the total variation of the unit normal vector field serves as a
regularizing functional to achieve these goals. In order to solve the resulting
problem, we use a version of the split Bregman (ADMM) iteration adapted to the
problem. A new formulation of the total variation regularizer, as well as the
use of an inexact Newton method for the shape optimization step, bring
significant speed-up compared to earlier methods. Numerical examples are
included, demonstrating the performance of our algorithm with some complex 3D
geometries.
