{"paper":{"title":"Data recovery: from limited-aperture to full-aperture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Jiguang Sun, XiaoDong Liu","submitted_at":"2017-08-09T22:49:33Z","abstract_excerpt":"The inverse scattering problems have been popular for the past thirty years. While very successful in many cases, progress has lagged when only {\\em limited-aperture} measurement is available. In this paper, we perform some elementary study to recover data that can not be measured directly. To be precise, we aim at recovering the {\\em full-aperture} far field data from {\\em limited-aperture} measurement. Due to the reciprocity relation, the multi-static response matrix (MSR) has a symmetric structure. Using the Green's formula and single layer potential, we propose two schemes to recover {\\em "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03029","kind":"arxiv","version":3},"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"}