Calculus of Variations and Geometric Measure Theory

Y. De Castro - V. Duval - R. Petit

Towards off-the-grid algorithms for total variation regularized inverse problems

created by petit on 29 Jun 2024
modified on 19 Jun 2025

[BibTeX]

Published Paper

Inserted: 29 jun 2024
Last Updated: 19 jun 2025

Journal: Journal of Mathematical Imaging and Vision
Year: 2023
Doi: https://doi.org/10.1007/s10851-022-01115-w

ArXiv: 2104.06706 PDF

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.