{"paper":{"title":"Coercive functions from a topological viewpoint and properties of minimizing sets of convex functions appearing in image restoration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.CA","math.FA"],"primary_cat":"math.OC","authors_text":"Ren\\'e Ciak","submitted_at":"2015-06-23T18:16:41Z","abstract_excerpt":"Many tasks in image processing can be tackled by modeling an appropriate data fidelity term $\\Phi: \\mathbb{R}^n \\rightarrow \\mathbb{R} \\cup \\{+\\infty\\}$ and then solve one of the regularized minimization problems \\begin{align*}\n  &{}(P_{1,\\tau}) \\qquad \\mathop{\\rm argmin}_{x \\in \\mathbb R^n} \\big\\{ \\Phi(x) \\;{\\rm s.t.}\\; \\Psi(x) \\leq \\tau \\big\\} \\\\ &{}(P_{2,\\lambda}) \\qquad \\mathop{\\rm argmin}_{x \\in \\mathbb R^n} \\{ \\Phi(x) + \\lambda \\Psi(x) \\}, \\; \\lambda > 0 \\end{align*} with some function $\\Psi: \\mathbb{R}^n \\rightarrow \\mathbb{R} \\cup \\{+\\infty\\}$ and a good choice of the parameter(s). Two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08615","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"}