{"paper":{"title":"On unified view of nullspace-type conditions for recoveries associated with general sparsity structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"math.OC","authors_text":"Anatoli Juditsky, Arkadi Nemirovski, Fatma Kilinc Karzan","submitted_at":"2012-07-04T20:34:12Z","abstract_excerpt":"We discuss a general notion of \"sparsity structure\" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the \"usual sparsity\" and \"usual $\\ell_1$ recovery,\" (b) block-sparsity with possibly overlapping blocks and associated block-$\\ell_1$ recovery, and (c) low-rank-oriented recovery by nuclear norm minimization. The proposed recovery routines are natural extensions of the usual $\\ell_1$ minimization used in Compressed Sensing. Specifically we present nullspace-type sufficient cond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1119","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"}