{"paper":{"title":"Image Processing Variations with Analytic Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"John B. Garnett, Luminita A. Vese, Triet M. Le","submitted_at":"2012-04-05T00:11:56Z","abstract_excerpt":"Let $f\\in L^1(\\R^d)$ be real. The Rudin-Osher-Fatemi model is to minimize $\\|u\\|_{\\dot{BV}}+\\lambda\\|f-u\\|_{L^2}^2$, in which one thinks of $f$ as a given image, $\\lambda > 0$ as a \"tuning parameter\", $u$ as an optimal \"cartoon\" approximation to $f$, and $f-u$ as \"noise\" or \"texture\". Here we study variations of the R-O-F model having the form $\\inf_u\\{\\|u\\|_{\\dot{BV}}+\\lambda \\|K*(f-u)\\|_{L^p}^q\\}$ where $K$ is a real analytic kernel such as a Gaussian. For these functionals we characterize the minimizers $u$ and establish several of their properties, including especially their smoothness pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1097","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"}