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

Yohann De Castro; Vincent Duval; Romain Petit

doi:10.1007/s10851-022-01115-w

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

Yohann De Castro
, Vincent Duval
, Romain Petit

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	53-81
Number of pages	29
Journal	Journal of Mathematical Imaging and Vision
Volume	65
Issue number	1
DOIs	https://doi.org/10.1007/s10851-022-01115-w
Publication status	Published - 1 Jan 2023
Externally published	Yes

Keywords

Inverse problems
Off-the-grid imaging
Total variation

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10.1007/s10851-022-01115-w

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title = "Towards Off-the-Grid Algorithms for Total Variation Regularized Inverse Problems",

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.",

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AB - 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.

KW - Inverse problems

KW - Off-the-grid imaging

KW - Total variation

UR - https://www.scopus.com/pages/publications/85136235172

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

Abstract

Keywords

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