{"paper":{"title":"Infimal Convolution Regularisation Functionals of BV and $\\mathrm{L}^{p}$ Spaces. The Case p$=\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carola-Bibiane Sch\\\"onlieb, Evangelos Papoutsellis, Konstantinos Papafitsoros, Martin Burger","submitted_at":"2015-10-30T10:03:59Z","abstract_excerpt":"In this paper we analyse an infimal convolution type regularisation functional called $\\mathrm{TVL}^{\\infty}$, based on the total variation ($\\mathrm{TV}$) and the $\\mathrm{L}^{\\infty}$ norm of the gradient. The functional belongs to a more general family of $\\mathrm{TVL}^{p}$ functionals ($1<p\\le \\infty$). We show via analytical and numerical results that the minimisation of the $\\mathrm{TVL}^{\\infty}$ functional promotes piecewise affine structures in the reconstructed images similar to the state of the art total generalised variation ($\\mathrm{TGV}$) but improving upon preservation of hat--"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.09032","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"}