{"paper":{"title":"Projection onto the Cosparse Set is NP-Hard","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andreas M. Tillmann, Marc E. Pfetsch, R\\'emi Gribonval (INRIA - IRISA)","submitted_at":"2013-03-21T15:42:18Z","abstract_excerpt":"The computational complexity of a problem arising in the context of sparse optimization is considered, namely, the projection onto the set of $k$-cosparse vectors w.r.t. some given matrix $\\Omeg$. It is shown that this projection problem is (strongly) \\NP-hard, even in the special cases in which the matrix $\\Omeg$ contains only ternary or bipolar coefficients. Interestingly, this is in contrast to the projection onto the set of $k$-sparse vectors, which is trivially solved by keeping only the $k$ largest coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5305","kind":"arxiv","version":2},"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"}