{"paper":{"title":"Infimal convolution regularisation functionals of BV and $\\mathrm{L}^{p}$ spaces. Part I: The finite $p$ case","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":"2015-04-08T13:28:33Z","abstract_excerpt":"We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation ($\\mathrm{TV}$) seminorm and $\\mathrm{L}^{p}$ norms. A unified well-posedness analysis is presented and a detailed study of the one dimensional model is performed, by computing exact solutions for the corresponding denoising problem and the case $p=2$. Furthermore, the dependency of the regularisation properties of this infimal convolution approach to the choice of $p$ is studied. It turns out that in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01956","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"}