Quantitative analysis of finite-difference approximations of free-discontinuity problems
Annika Bach
Technische Universität München, Garching, GermanyAndrea Braides
Università di Roma Tor Vergata, ItalyCaterina Ida Zeppieri
Universität Münster, Germany
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Abstract
Motivated by applications to image reconstruction, in this paper we analyse a finite-difference discretisation of the Ambrosio–Tortorelli functional. Denoted by the elliptic-approximation parameter and by the discretisation step-size, we fully describe the relative impact of and in terms of -limits for the corresponding discrete functionals, in the three possible scaling regimes. We show, in particular, that when and are of the same order, the underlying lattice structure affects the -limit which turns out to be an anisotropic free-discontinuity functional.
Cite this article
Annika Bach, Andrea Braides, Caterina Ida Zeppieri, Quantitative analysis of finite-difference approximations of free-discontinuity problems. Interfaces Free Bound. 22 (2020), no. 3, pp. 317–381
DOI 10.4171/IFB/443