{"paper":{"title":"SUPER: Sparse signals with Unknown Phases Efficiently Recovered","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mayank Bakshi, Minghua Chen, Sheng Cai, Sidharth Jaggi","submitted_at":"2014-01-17T08:34:17Z","abstract_excerpt":"Suppose ${\\bf x}$ is any exactly $k$-sparse vector in $\\mathbb{C}^{n}$. We present a class of phase measurement matrix $A$ in $\\mathbb{C}^{m\\times n}$, and a corresponding algorithm, called SUPER, that can resolve ${\\bf x}$ up to a global phase from intensity measurements $|A{\\bf x}|$ with high probability over $A$. Here $|A{\\bf x}|$ is a vector of component-wise magnitudes of $A{\\bf x}$. The SUPER algorithm is the first to simultaneously have the following properties: (a) it requires only ${\\cal O}(k)$ (order-optimal) measurements, (b) the computational complexity of decoding is ${\\cal O}(k\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4269","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"}