{"paper":{"title":"Capacity-Approaching PhaseCode for Low-Complexity Compressive Phase Retrieval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kangwook Lee, Kannan Ramchandran, Ramtin Pedarsani","submitted_at":"2014-12-18T01:21:22Z","abstract_excerpt":"In this paper, we tackle the general compressive phase retrieval problem. The problem is to recover a K-sparse complex vector of length n, $x\\in \\mathbb{C}^n$, from the magnitudes of m linear measurements, $y=|Ax|$, where $A \\in \\mathbb{C}^{m \\times n}$ can be designed, and the magnitudes are taken component-wise for vector $Ax\\in \\mathbb{C}^m$. We propose a variant of the PhaseCode algorithm, and show that, using an irregular left-degree sparse-graph code construction, the algorithm can recover almost all the K non-zero signal components using only slightly more than 4K measurements under som"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5694","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"}