Imaging and image processing in porous media research

A Kaestner, E Lehmann, M Stampanoni - Advances in Water Resources, 2008 - Elsevier
Three-dimensional imaging and image processing has become an important part for
investigations of fluid distribution and flow in porous media. We describe two methods of …

Theoretical foundations for discrete forward-and-backward diffusion filtering

M Welk, G Gilboa, J Weickert - … Conference on Scale Space and Variational …, 2009 - Springer
Abstract Forward-and-backward (FAB) diffusion is a method for sharpening blurry images
(Gilboa et al. 2002). It combines forward diffusion with a positive diffusivity and backward …

PDE evolutions for M-smoothers in one, two, and three dimensions

M Welk, J Weickert - Journal of Mathematical Imaging and Vision, 2021 - Springer
Local M-smoothers are interesting and important signal and image processing techniques
with many connections to other methods. In our paper, we derive a family of partial …

A discrete theory and efficient algorithms for forward-and-backward diffusion filtering

M Welk, J Weickert, G Gilboa - Journal of Mathematical Imaging and Vision, 2018 - Springer
Image enhancement with forward-and-backward (FAB) diffusion lacks a sound theory and is
numerically very challenging due to its diffusivities that are negative within a certain gradient …

Regularised Diffusion–Shock Inpainting

K Schaefer, J Weickert - Journal of Mathematical Imaging and Vision, 2024 - Springer
We introduce regularised diffusion–shock (RDS) inpainting as a modification of diffusion–
shock inpainting from our SSVM 2023 conference paper. RDS inpainting combines two …

Enhanced total variation minimization for stable image reconstruction

C An, HN Wu, X Yuan - Inverse Problems, 2023 - iopscience.iop.org
The total variation (TV) regularization has phenomenally boosted various variational models
for image processing tasks. We propose to combine the backward diffusion process in the …

Diffusion–Shock Inpainting

K Schaefer, J Weickert - International Conference on Scale Space and …, 2023 - Springer
We propose diffusion–shock (DS) inpainting as a hitherto unexplored integrodifferential
equation for filling in missing structures in images. It combines two carefully chosen …

[PDF][PDF] Implementation of shock filter for digital X-ray image processing

LR Dung, ST Sun, YY Wu - Journal of Computer and …, 2014 - pdfs.semanticscholar.org
X-ray image might be corrupted by noise or blurring because of signal transmission or the
bad X-ray lens. This paper presents a two-stage shock filter based on Partial Differential …

Conditional toggle map**s: principles and applications

S Velasco-Forero, J Angulo, P Soille - Journal of mathematical imaging …, 2014 - Springer
We study a class of mathematical morphology filters to operate conditionally according to a
set of pixels marked by a binary mask. The main contribution of this paper is to provide a …

[HTML][HTML] Staircasing in semidiscrete stabilised inverse linear diffusion algorithms

M Breuß, M Welk - Journal of Computational and Applied Mathematics, 2007 - Elsevier
We consider a semidiscrete model problem for the approximation of stabilised inverse linear
diffusion processes. The work is motivated by an important observation on fully discrete …