Higher-Order Total Directional Variation: Imaging Applications
Simone Parisotto, Jan Lellmann, Simon Masnou, Carola‐Bibiane Schönlieb · SIAM Journal on Imaging Sciences · 2020
We introduce a class of higher-order anisotropic total variation regularizers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the total generalized variation regularizer and its variants. We propose a primal-dual hybrid gradient approach to approximating numerically the associated gradient flow. This choice of regularizers allows us 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.