{"paper":{"title":"Compressive sensing and truncated moment problems on spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Camilo Hern\\'andez, Hern\\'an Garc\\'ia, Mauricio Junca, Mauricio Velasco","submitted_at":"2017-10-25T23:57:28Z","abstract_excerpt":"We propose convex optimization algorithms to recover a good approximation of a point measure $\\mu$ on the unit sphere $S\\subseteq \\mathbb{R}^n$ from its moments with respect to a set of real-valued functions $f_1,\\dots, f_m$. Given a finite subset $C\\subseteq S$ the algorithm produces a measure $\\mu^*$ supported on $C$ and we prove that $\\mu^*$ is a good approximation to $\\mu$ whenever the functions $f_1,\\dots, f_m$ are a sufficiently large random sample of independent Kostlan-Shub-Smale polynomials. More specifically, we give sufficient conditions for the validity of the equality $\\mu=\\mu^*$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09496","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"}