{"paper":{"title":"Inverting Spherical Radon Transform by a Closed-form Formula: A Microlocal Analytic Point of View","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Linh V. Nguyen","submitted_at":"2013-07-10T00:20:41Z","abstract_excerpt":"Let $\\mR$ be the restriction of the spherical Radon transform to the set of spheres centered on a hypersurface $\\mS$. We study the inversion of $\\mR$ by a closed-form formula. We approach the problem by studying an oscillatory integral, which depends on the observation surface $\\mS$ as a parameter. We then derive various microlocal analytic properties of the associated closed-form inversion formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2634","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":""},"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"}