{"paper":{"title":"Exact Reconstruction of Spatially Undersampled Signals in Evolutionary Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"cs.OH","authors_text":"Akram Aldroubi, Ilya Krishtal, Jacqueline Davis","submitted_at":"2013-12-04T19:52:24Z","abstract_excerpt":"We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\\{t_1,\\dots,t_N\\}$. This new way of sampling, which we call dynamical sampling, differs from standard sampling since at any fixed time $t_i$ there are not enough samples to recover the function $f$ or the state $f_{t_i}$. Although dynamical sampling is an inverse problem, it differs from the typical inverse problems in which $f$ is to be recovered from $A_Tf$ for a single time $T$. In this paper, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3203","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"}