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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1704.00451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-03T07:11:07Z","cross_cats_sorted":[],"title_canon_sha256":"c3dc6f8deb0c447949463a71b9ca3f5ab74ff9b775400140fd5a5f598aad2308","abstract_canon_sha256":"f2cca4cbb4a93300e5b3d08cf8bd273bdd0f3b8462bea45780682522c3c2bd91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:24.441420Z","signature_b64":"V3/GmgCLtTlfwRjShOYyjC0y1KgjPvo6jH6AOJUlKRK+k65SgE2Wdl88zbB97EcDxUWoIJn/u5rWKINX5F+UDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"141186ff7ae7629f98334c3fafc11c4331125a78188151f4ec646eb24b201e43","last_reissued_at":"2026-05-18T00:47:24.440708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:24.440708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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