{"paper":{"title":"Asymptotic behaviour of total generalised variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Konstantinos Papafitsoros, Tuomo Valkonen","submitted_at":"2015-02-24T20:14:05Z","abstract_excerpt":"The recently introduced second order total generalised variation functional $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ has been a successful regulariser for image processing purposes. Its definition involves two positive parameters $\\alpha$ and $\\beta$ whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of $\\mathrm{TGV}_{\\beta,\\alpha}^{2}$ in the cases where the parameters $\\alpha, \\beta$ as well as their ratio $\\beta/\\alpha$ becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and lar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06933","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"}