{"paper":{"title":"The global landscape of phase retrieval I: perturbed amplitude models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.NA","math.IT"],"primary_cat":"math.NA","authors_text":"Dong Li, Jian-Feng Cai, Meng Huang, Yang Wang","submitted_at":"2021-12-15T09:40:04Z","abstract_excerpt":"A fundamental task in phase retrieval is to recover an unknown signal $\\vx\\in \\Rn$ from a set of magnitude-only measurements $y_i=\\abs{\\nj{\\va_i,\\vx}}, \\; i=1,\\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs) which have non-convex and quadratic-type loss function. When the measurements $ \\va_i \\in \\Rn$ are Gaussian random vectors and the number of measurements $m\\ge Cn$, we rigorously prove that the PAMs admit no spurious local minimizers with high probability, i.e., the target solution $ \\vx$ is the unique global minimizer (up to a global phase) and the loss fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.07993","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.07993/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}