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


Published Paper

Inserted: 29 jun 2024
Last Updated: 29 jun 2024

Journal: Journal of Mathematical Imaging and Vision
Year: 2021

ArXiv: 2104.06706 PDF


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.