{"paper":{"title":"New Conditions for Sparse Phase Retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA","math.OC"],"primary_cat":"cs.IT","authors_text":"Mehmet Ak\\c{c}akaya, Vahid Tarokh","submitted_at":"2013-10-04T18:13:07Z","abstract_excerpt":"We consider the problem of sparse phase retrieval, where a $k$-sparse signal ${\\bf x} \\in {\\mathbb R}^n \\textrm{ (or } {\\mathbb C}^n\\textrm{)}$ is measured as ${\\bf y} = |{\\bf Ax}|,$ where ${\\bf A} \\in {\\mathbb R}^{m \\times n} \\textrm{ (or } {\\mathbb C}^{m \\times n}\\textrm{ respectively)}$ is a measurement matrix and $|\\cdot|$ is the element-wise absolute value. For a real signal and a real measurement matrix ${\\bf A}$, we show that $m = 2k$ measurements are necessary and sufficient to recover ${\\bf x}$ uniquely. For complex signal ${\\bf x} \\in {\\mathbb C}^n$ and ${\\bf A} \\in {\\mathbb C}^{m \\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1351","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"}