{"paper":{"title":"Limiting aspects of non-convex ${TV}^\\phi$ models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.FA","authors_text":"Michael Hinterm\\\"uller, Tao Wu, Tuomo Valkonen","submitted_at":"2014-12-23T22:50:34Z","abstract_excerpt":"Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\\phi$ in the total variation type functional ${TV}^\\phi(u) := \\int \\phi(|\\nabla u(x)|) d x$. In this paper, it is demonstrated that for typical choices of $\\phi$, functionals of this type pose several difficulties when extended to the entire space of functions of bounded variation, ${BV}(\\Omega)$. In particular, if $\\phi(t)=t^q$ for $q \\in (0, 1)$ and ${TV}^\\phi$ is defined directly for piecewise constant functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7572","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1412.7572/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}