{"paper":{"title":"Phaseless Reconstruction from Space-Time Samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.FA","authors_text":"Akram Aldroubi, llya krishtal, Sui Tang","submitted_at":"2017-06-16T17:32:55Z","abstract_excerpt":"Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\\mathcal{H}$ from the modulus of linear measurements $\\{\\lvert \\langle x, \\phi_i\\rangle \\rvert$, $ \\ldots$, $\\lvert \\langle A^{L_i}x, \\phi_i \\rangle \\rvert : i \\in\\mathscr I\\}$, where $\\{\\phi_i; i \\in\\mathscr I\\}\\subset \\mathcal{H}$ is a set of functionals on $\\mathcal{H}$, and $A$ is a bounded operator on $\\mathcal{H}$ that acts as an evolution operator. In this paper, we provide various sufficient or necessary conditions for solving this problem, which has connections to $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05360","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"}