Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems
Signal Processing
2025-07-08 v5 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed mesh, our approach exploits the structure of the solutions and consists in iteratively constructing a linear combination of indicator functions of simple polygons.
Cite
@article{arxiv.2104.06706,
title = {Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems},
author = {Yohann de Castro and Vincent Duval and Romain Petit},
journal= {arXiv preprint arXiv:2104.06706},
year = {2025}
}
Comments
For the short conference version see arXiv:2104.06706v2. For the long journal version see arXiv:2104.06706v5