33 citations · 89 across the 29 of their papers we have counts for
11 papers · 1 filter
Grid is Good: Adaptive Refinement Algorithms for Off-the-Grid Total Variation Minimization
Axel Flinth, Frédéric de Gournay, Pierre Weiss
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube…
Spurious minimizers in non uniform Fourier sampling optimization
Frédéric de Gournay, Alban Gossard, Pierre Weiss
A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing op…
On the linear convergence rates of exchange and continuous methods for total variation minimization
Axel Flinth, Frédéric de Gournay, Pierre Weiss
We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M() of Radon measures on a subset of R d. Our main re…
Convex Regularization and Representer Theorems
Claire Boyer, Antonin Chambolle, Yohann de Castro +3
We establish a result which states that regularizing an inverse problem with the gauge of a convex set yields solutions which are linear combinations of a few extreme points or…
On Representer Theorems and Convex Regularization
Claire Boyer, Antonin Chambolle, Yohann De Castro +3
We establish a general principle which states that regularizing an inverse problem with a convex function yields solutions which are convex combinations of a small number of atoms.…
Exact solutions of infinite dimensional total-variation regularized problems
Axel Flinth, Pierre Weiss
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to…