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Book Sections Year : 2021

Approximating the Total Variation with Finite Differences or Finite Elements

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Abstract

We present and compare various types of discretizations which have been proposed to approximate the total variation (mostly, of a grey-level image in two dimensions). We discuss the properties of finite differences and finite elements based approach and compare their merits, in particular in terms of error estimates and quality of the reconstruction.
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Dates and versions

hal-02959358 , version 1 (06-10-2020)
hal-02959358 , version 2 (28-10-2020)

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Antonin Chambolle, Thomas Pock. Approximating the Total Variation with Finite Differences or Finite Elements. Handbook of Numerical Analysis: Geometric Partial Differential Equations II, 22, , pp.383--417, 2021, Handbook of Numerical Analysis: Geometric Partial Differential Equations II, ISSN 1570-8659. ⟨10.1016/bs.hna.2020.10.005⟩. ⟨hal-02959358v2⟩
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