{"paper":{"title":"Exact Reconstruction Formula for the Spherical Mean Radon Transform on Ellipsoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Haltmeier","submitted_at":"2014-04-15T14:41:28Z","abstract_excerpt":"Many modern imaging and remote sensing applications require reconstructing a function from spherical averages (mean values). Examples include photoacoustic tomography, ultrasound imaging or SONAR. Several formulas of the back-projection type for recovering a function in $n$ spatial dimensions from mean values over spheres centered on a sphere have been derived in [D. Finch, S. K. Patch, and Rakesh, SIAM J. Math. Anal. 35(5), pp. 1213--1240, 2004] for odd spatial dimension and in [D. Finch, M. Haltmeier, and Rakesh, SIAM J. Appl. Math. 68(2), pp. 392--412, 2007] for even spatial dimension. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3935","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":""},"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"}