# Higher-Order Total Directional Variation: Imaging Applications

## TL;DR

This paper introduces higher-order anisotropic total variation regularisers that extend TGV, enabling better preservation of anisotropic features in images across various applications like denoising and surface reconstruction.

## Contribution

It presents a new class of regularisers for imaging that generalize TGV to anisotropic, inhomogeneous cases, with a numerical approach for gradient flow approximation.

## Key findings

- Enhanced anisotropic feature preservation in images
- Effective application to denoising, zooming, and surface reconstruction
- Numerical method demonstrates practical viability

## Abstract

We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We propose a primal-dual hybrid gradient approach to approximate numerically the associated gradient flow. This choice of regularisers allows to preserve and enhance intrinsic anisotropic features in images. This is illustrated on various examples from different imaging applications: image denoising, wavelet-based image zooming, and reconstruction of surfaces from scattered height measurements.