{"paper":{"title":"Precisely Verifying the Null Space Conditions in Compressed Sensing: A Sandwiching Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","math.IT","math.OC","stat.ML"],"primary_cat":"cs.IT","authors_text":"Myung Cho, Weiyu Xu","submitted_at":"2013-06-11T21:57:47Z","abstract_excerpt":"In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an $(n-m) \\times n$ ($m>0$) CS matrix $A$ and a positive $k$, we are interested in computing $\\displaystyle \\alpha_k = \\max_{\\{z: Az=0,z\\neq 0\\}}\\max_{\\{K: |K|\\leq k\\}}$ ${\\|z_K \\|_{1}}{\\|z\\|_{1}}$, where $K$ represents subsets of $\\{1,2,...,n\\}$, and $|K|$ is the cardinality of $K$. In particular, we are interested in finding the maximum $k$ such that $\\alpha_k < {1}{2}$. However, computing $\\alpha_k$ is known to be extremely challenging. In this paper, we first propose a se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2665","kind":"arxiv","version":3},"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"}