{"paper":{"title":"On Gradient Descent Algorithm for Generalized Phase Retrieval Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ji Li, Tie Zhou","submitted_at":"2016-07-05T05:51:53Z","abstract_excerpt":"In this paper, we study the generalized phase retrieval problem: to recover a signal $\\bm{x}\\in\\mathbb{C}^n$ from the measurements $y_r=\\lvert \\langle\\bm{a}_r,\\bm{x}\\rangle\\rvert^2$, $r=1,2,\\ldots,m$. The problem can be reformulated as a least-squares minimization problem. Although the cost function is nonconvex, the global convergence of gradient descent algorithm from a random initialization is studied, when $m$ is large enough. We improve the known result of the local convergence from a spectral initialization. When the signal $\\bm{x}$ is real-valued, we prove that the cost function is loca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01121","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"}