{"paper":{"title":"Reshaped Wirtinger Flow and Incremental Algorithm for Solving Quadratic System of Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Huishuai Zhang, Yingbin Liang, Yi Zhou, Yuejie Chi","submitted_at":"2016-05-25T03:45:44Z","abstract_excerpt":"We study the phase retrieval problem, which solves quadratic system of equations, i.e., recovers a vector $\\boldsymbol{x}\\in \\mathbb{R}^n$ from its magnitude measurements $y_i=|\\langle \\boldsymbol{a}_i, \\boldsymbol{x}\\rangle|, i=1,..., m$. We develop a gradient-like algorithm (referred to as RWF representing reshaped Wirtinger flow) by minimizing a nonconvex nonsmooth loss function. In comparison with existing nonconvex Wirtinger flow (WF) algorithm \\cite{candes2015phase}, although the loss function becomes nonsmooth, it involves only the second power of variable and hence reduces the complexi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.07719","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"}