Towards Off-the-grid Algorithms for Total Variation Regularized Inverse Problems

TL;DR

This paper presents a novel gridless algorithm for solving inverse problems with total variation regularization, constructing solutions as combinations of polygon indicators, unlike traditional mesh-based methods.

Contribution

The paper introduces a gridless, iterative algorithm that constructs solutions as linear combinations of polygon indicator functions for total variation regularized inverse problems.

Findings

Algorithm effectively constructs solutions as polygon indicators.

Method outperforms traditional mesh-based approaches.

Provides a new perspective on gridless inverse problem solving.

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.