{"paper":{"title":"A class of null space conditions for sparse recovery via nonconvex, non-separable minimizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Clayton Webster, Hoang Tran","submitted_at":"2017-10-19T20:49:08Z","abstract_excerpt":"For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than $\\ell_1$ penalty in enhancing the sparsity of solution. However, to date, the theory verifying that nonconvex penalties outperform (or are at least as good as) $\\ell_1$ minimization in exact, uniform recovery has mostly been limited to separable cases. In this paper, we establish general recovery guarantees through null space conditions for nonconvex, non-separable regularizations, which are slightly less demanding than the standard null space property for $\\ell_1$ minimization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07348","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"}