{"paper":{"title":"Compressive Phase Retrieval via Generalized Approximate Message Passing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Philip Schniter, Sundeep Rangan","submitted_at":"2014-05-22T03:02:17Z","abstract_excerpt":"In phase retrieval, the goal is to recover a signal $\\mathbf{x}\\in\\mathbb{C}^N$ from the magnitudes of linear measurements $\\mathbf{Ax}\\in\\mathbb{C}^M$. While recent theory has established that $M\\approx 4N$ intensity measurements are necessary and sufficient to recover generic $\\mathbf{x}$, there is great interest in reducing the number of measurements through the exploitation of sparse $\\mathbf{x}$, which is known as compressive phase retrieval. In this work, we detail a novel, probabilistic approach to compressive phase retrieval based on the generalized approximate message passing (GAMP) a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5618","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"}