{"paper":{"title":"Lossless Linear Analog Compression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Camillo De Lellis, Erwin Riegler, Giovanni Alberti, G\\\"unther Koliander, Helmut B\\\"olcskei","submitted_at":"2016-05-03T13:54:40Z","abstract_excerpt":"We establish the fundamental limits of lossless linear analog compression by considering the recovery of random vectors ${\\boldsymbol{\\mathsf{x}}}\\in{\\mathbb R}^m$ from the noiseless linear measurements ${\\boldsymbol{\\mathsf{y}}}=\\boldsymbol{A}{\\boldsymbol{\\mathsf{x}}}$ with measurement matrix $\\boldsymbol{A}\\in{\\mathbb R}^{n\\times m}$. Specifically, for a random vector ${\\boldsymbol{\\mathsf{x}}}\\in{\\mathbb R}^m$ of arbitrary distribution we show that ${\\boldsymbol{\\mathsf{x}}}$ can be recovered with zero error probability from $n>\\inf\\underline{\\operatorname{dim}}_\\mathrm{MB}(U)$ linear measu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00912","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"}