{"paper":{"title":"Characterization of minimizers of an anisotropic variant of the Rudin-Osher-Fatemi functional with $L^1$ fidelity term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nils Dabrock","submitted_at":"2017-04-03T07:11:07Z","abstract_excerpt":"In this paper we study an anisotropic variant of the Rudin-Osher-Fatemi functional with $L^1$ fidelity term of the form \\[ E(u) = \\int_{\\mathbb{R}^n} \\phi(\\nabla u) + \\lambda \\| u -f \\|_{L^1(\\mathbb{R}^n)}. \\] We will characterize the minimizers of $E$ in terms of the Wulff shape of $\\phi$ and the dual anisotropy. In particular we will calculate the subdifferential of $E$. We will apply this characterization to the special case $\\phi = |\\cdot|_1$ and $n=2$, which has been used in the denoising of 2D bar codes. In this case, we determine the shape of a minimizer $u$ when $f$ is the characterist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00451","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}