{"paper":{"title":"A multi-frequency sampling method for the inverse source problems with sparse measurements","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Shixu Meng, XiaoDong Liu","submitted_at":"2021-09-03T10:52:19Z","abstract_excerpt":"We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced based on the integral over the frequency variable. A factorization of this multi-frequency near field operator is further given and analysed. Motivated by such a factorization, we introduce a multi-frequency sampling method to reconstruct the source support. Its theoretical foundation is then derived from the properties of the factorized operators and a prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.01434","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/2109.01434/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"}