{"paper":{"title":"Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Gil Goldman, Yehonatan Salman, Yosef Yomdin","submitted_at":"2018-01-07T12:09:25Z","abstract_excerpt":"This is a survey paper discussing one specific (and classical) system of algebraic equations - the so called \"Prony system\". We provide a short overview of its unusually wide connections with many different fields of Mathematics, stressing the role of Singularity Theory. We reformulate Prony System as the problem of reconstruction of \"Spike-train\" signals of the form $F(x)=\\sum_{j=1}^d a_j\\delta(x-x_j)$ from the noisy moment measurements. We provide an overview of some recent results of [1-3, 6, 8, 9, 11, 12, 5] on the \"geometry of the error amplification\" in the reconstruction process, in sit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02177","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"}