{"paper":{"title":"Improved Algorithms for Adaptive Compressed Sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Hongyang Zhang, Vasileios Nakos, Xiaofei Shi","submitted_at":"2018-04-25T16:43:33Z","abstract_excerpt":"In the problem of adaptive compressed sensing, one wants to estimate an approximately $k$-sparse vector $x\\in\\mathbb{R}^n$ from $m$ linear measurements $A_1 x, A_2 x,\\ldots, A_m x$, where $A_i$ can be chosen based on the outcomes $A_1 x,\\ldots, A_{i-1} x$ of previous measurements. The goal is to output a vector $\\hat{x}$ for which $$\\|x-\\hat{x}\\|_p \\le C \\cdot \\min_{k\\text{-sparse } x'} \\|x-x'\\|_q\\,$$ with probability at least $2/3$, where $C > 0$ is an approximation factor. Indyk, Price and Woodruff (FOCS'11) gave an algorithm for $p=q=2$ for $C = 1+\\epsilon$ with $\\Oh((k/\\epsilon) \\loglog (n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09673","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"}