{"paper":{"title":"$L^2$-stability analysis for Gabor phase retrieval","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Martin Rathmair, Philipp Grohs","submitted_at":"2021-08-13T10:11:56Z","abstract_excerpt":"We consider the problem of reconstructing the missing phase information from spectrogram data $|\\mathcal{G} f|,$ with $$ \\mathcal{G}f(x,y)=\\int_\\mathbb{R} f(t) e^{-\\pi(t-x)^2}e^{-2\\pi i t y}dt, $$ the Gabor transform of a signal $f\\in L^2(\\mathbb{R})$. More specifically, we are interested in domains $\\Omega\\subseteq \\mathbb{R}^2$, which allow for stable local reconstruction, that is $$ |\\mathcal{G}g| \\approx |\\mathcal{G}f| \\quad \\text{in} ~\\Omega \\quad\\Longrightarrow \\quad \\exists \\tau\\in\\mathbb{T}:\\quad \\mathcal{G}g \\approx \\tau\\mathcal{G}f \\quad \\text{in} ~\\Omega. $$ In recent work [P. Grohs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.06154","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/2108.06154/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"}