{"paper":{"title":"Stable Phase Retrieval in Infinite Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ingrid Daubechies, Philipp Grohs, Rima Alaifari, Rujie Yin","submitted_at":"2016-08-31T20:49:08Z","abstract_excerpt":"The problem of phase retrieval is to determine a signal $f\\in \\mathcal{H}$, with $\\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\\omega)|$, where $F(\\omega):=\\langle f , \\varphi_\\omega\\rangle$ are measurements of $f$ with respect to a measurement system $(\\varphi_\\omega)_{\\omega\\in \\Omega}\\subset \\mathcal{H}$. Although phase retrieval is always stable in the finite dimensional setting whenever it is possible (i.e. injectivity implies stability for the inverse problem), the situation is drastically different if $\\mathcal{H}$ is infinite-dimensional: in that case phase retrieval i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00034","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"}