English

Higher-Order Total Directional Variation: Imaging Applications

Numerical Analysis 2020-07-10 v4 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.1812.05023,
  title  = {Higher-Order Total Directional Variation: Imaging Applications},
  author = {Simone Parisotto and Jan Lellmann and Simon Masnou and Carola-Bibiane Schönlieb},
  journal= {arXiv preprint arXiv:1812.05023},
  year   = {2020}
}

Comments

42 pages, 16 figures

R2 v1 2026-06-23T06:40:23.511Z