24 citations · 79 across the 10 of their papers we have counts for
13 papers
Boundedness and unboundedness in total variation regularization
Kristian Bredies, José A. Iglesias, Gwenael Mercier
We consider whether minimizers for total variation regularization of linear inverse problems belong to even if the measured data does not. We present a simple proof of b…
Convergence of level sets in fractional Laplacian regularization
José A. Iglesias, Gwenael Mercier
The use of the fractional Laplacian in image denoising and regularization of inverse problems has enjoyed a recent surge in popularity, since for discontinuous functions it can beh…
Convergence of level sets in total variation denoising through variational curvatures in unbounded domains
José A. Iglesias, Gwenael Mercier
We present some results of geometric convergence of level sets for solutions of total variation denoising as the regularization parameter tends to zero. The common feature among th…
Inverse Problems of Single Molecule Localization Microscopy
Montse Lopez-Martinez, Gwenael Mercier, Kamran Sadiq +5
Single molecule localization microscopy is a recently developed superresolution imaging technique to visualize structural properties of single cells. The basic principle consists i…
Computing the Yield Limit in Three-dimensional Flows of a Yield Stress Fluid About a Settling Particle
José A. Iglesias, Gwenael Mercier, Emad Chaparian +1
Calculating the yield limit (the critical ratio of the yield stress to the driving stress), of a viscoplastic fluid flow is a challenging problem, often needing iteration in…
Influence of dimension on the convergence of level-sets in total variation regularization
José A. Iglesias, Gwenael Mercier
We extend some recent results on the Hausdorff convergence of level-sets for total variation regularized linear inverse problems. Dimensions higher than two and measurements in Ban…
Critical yield numbers and limiting yield surfaces of particle arrays settling in a Bingham fluid
José A. Iglesias, Gwenael Mercier, Otmar Scherzer
We consider the flow of multiple particles in a Bingham fluid in an anti-plane shear flow configuration. The limiting situation in which the internal and applied forces balance and…
A note on convergence of solutions of total variation regularized linear inverse problems
José A. Iglesias, Gwenael Mercier, Otmar Scherzer
In a recent paper by A. Chambolle et al. [Geometric properties of solutions to the total variation denoising problem. Inverse Problems 33, 2017] it was proven that if the subgradie…
Critical yield numbers of rigid particles settling in Bingham fluids and Cheeger sets
Ian A. Frigaard, José A. Iglesias, Gwenael Mercier +2
We consider the fluid mechanical problem of identifying the critical yield number of a dense solid inclusion (particle) settling under gravity within a bounded domain of Bing…
Continuity results for TV-minimizers
Gwenael Mercier
This paper deals with continuity preservation when minimizing generalized total variation with a fidelity term or a Dirichlet boundary condition. We extend several recent res…
Anisotropic curvature flow of immersed curves
Gwenael Mercier, Matteo Novaga, Paola Pozzi
We prove short-time existence of ϕ-regular solutions to the anisotropic and crystalline curvature flow of immersed planar curves.
Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions
Gwenael Mercier, Matteo Novaga
We show short time existence and uniqueness of $\C^{1,1}$ solutions to the mean curvature flow with obstacles, when the obstacles are of class $\C^{1,1}$. If the initial interface…
Mean curvature flow with obstacles: a viscosity approach
Gwenael Mercier
We introduce a level-set formulation for the mean curvature flow with obstacles and show existence and uniqueness of a viscosity solution. These results generalize a well known vis…