Researcher: Simone Parisotto, Carola-Bibiane Schönlieb

In this project, we introduce a new higher-order total directional variation (TDV) regulariser for inverse imaging problems by taking into account the image gradient weighted by the structural content. Theoretical and numerical details are provided for different applications: the reconstruction of noisy images and videos, the image zooming and the interpolation of scattered surface data. The idea of using directional gradients for imaging applications is also used for the generalisation of the osmosis equation, introduced by Weickert and collaborators in 2013, to its anisotropic counter-part. Anisotropic osmosis is applied to the shadow removal problem thus improving upon the isotropic approach by avoiding the blurring artefact due to the isotropic diffusion.