{"paper":{"title":"The estimation performance of nonlinear least squares for phase retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Meng Huang, Zhiqiang Xu","submitted_at":"2019-04-22T03:50:49Z","abstract_excerpt":"Suppose that $\\mathbf{y}=\\lvert A\\mathbf{x_0}\\rvert+\\eta$ where $\\mathbf{x_0} \\in \\mathbb{R}^d$ is the target signal and $\\eta\\in \\mathbb{R}^m$ is a noise vector. The aim of phase retrieval is to estimate $\\mathbf{x_0}$ from $\\mathbf{y}$. A popular model for estimating $\\mathbf{x_0} $ is the nonlinear least square $ \\widehat{\\mathbf{x}}:={\\rm argmin}_{\\mathbf{x}} \\| \\lvert A \\mathbf{x}\\rvert-\\mathbf{y}\\|_2$. One already develops many efficient algorithms for solving the model, such as the seminal error reduction algorithm. In this paper, we present the estimation performance of the model with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09711","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"}