TL;DR
This paper investigates the continuity properties of TV-minimizers with $L^2$ fidelity or Dirichlet boundary conditions, extending recent results by establishing comparison principles for their level-sets.
Contribution
It extends existing results by proving comparison principles for the level-sets of TV-minimizers under specific boundary conditions.
Findings
Comparison principles for level-sets of TV-minimizers
Continuity preservation under $L^2$ fidelity or Dirichlet conditions
Extension of recent theoretical results
Abstract
This paper deals with continuity preservation when minimizing generalized total variation with a fidelity term or a Dirichlet boundary condition. We extend several recent results in the two cases, mainly by showing comparison principles for the prescribed mean curvature problem satisfied by the level-sets of such minimizers.
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