{"paper":{"title":"Recovering rank-one matrices via rank-r matrices relaxation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hung Hung, Pengwen Chen","submitted_at":"2014-05-07T01:33:13Z","abstract_excerpt":"PhaseLift, proposed by E.J. Cand\\`{e}s et al., is one convex relaxation approach for phase retrieval. The relaxation enlarges the solution set from rank one matrices to positive semidefinite matrices.\n  In this paper, a relaxation is employed to nonconvex alternating minimization methods to recover the rank-one matrices.\n  A generic measurement matrix can be standardized to a matrix consisting of orthonormal columns. To recover the rank-one matrix, the standardized frames are used to select the matrix with the maximal leading eigenvalue among the rank-$r$ matrices. Empirical studies are conduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1483","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"}