{"paper":{"title":"The high resolution sampling methods for acoustic sources from multi-frequency far field patterns at sparse observation directions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.AP","math.MP"],"primary_cat":"math.NA","authors_text":"Qingxiang Shi, XiaoDong Liu","submitted_at":"2024-08-16T09:55:38Z","abstract_excerpt":"This work is dedicated to novel uniqueness results and high resolution sampling methods for source support from multi-frequency sparse far field patterns. With a single pair of observation directions $\\pm\\hat{x}$, we prove that the lines $\\{z\\in\\mathbb R^2|\\, \\hat{x}\\cdot z = \\hat{x}\\cdot y, \\,y\\in A_{\\hat{x}}\\}$ can be determined by multi-frequency far field patterns at the directions $\\pm\\hat{x}$, where $A_{\\hat{x}}$ denotes a set containing the corners of the boundary and points whose normal vector to the boundary is parallel to $\\hat{x}$. Furthermore, if the source support is composed of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10829","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.10829/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"}