{"paper":{"title":"Imaging with highly incomplete and corrupted data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA","physics.comp-ph"],"primary_cat":"eess.IV","authors_text":"Alexei Novikov, Chrysoula Tsogka, George Papanicolaou, Miguel Moscoso","submitted_at":"2019-08-05T06:03:59Z","abstract_excerpt":"We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \\, \\rho =b$, where $A$ is an $N\\times K$ measurement matrix. We assume that the dimension of the unknown sparse vector $\\rho \\in {\\mathbb{C}}^K$ is much larger than the dimension of the data vector $b \\in {\\mathbb{C}}^N$, i.e, $K \\gg N$. We provide a theoretical framework that allows us to examine under what conditions the $\\ell_1$-minimization problem admits a solution that is close to the exact one in the presence of noise. Ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01479","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01479/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}