{"paper":{"title":"Phase retrieval from the norms of affine transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.IT"],"primary_cat":"cs.IT","authors_text":"Meng Huang, Zhiqiang Xu","submitted_at":"2018-05-21T05:43:27Z","abstract_excerpt":"In this paper, we consider the generalized phase retrieval from affine measurements. This problem aims to recover signals ${\\mathbf x} \\in {\\mathbb F}^d$ from the affine measurements $y_j=\\norm{M_j^*\\vx +{\\mathbb b}_j}^2,\\; j=1,\\ldots,m,$ where $M_j \\in {\\mathbb F}^{d\\times r}, {\\mathbf b}_j\\in {\\mathbb F}^{r}, {\\mathbb F}\\in \\{{\\mathbb R},{\\mathbb C}\\}$ and we call it as {\\em generalized affine phase retrieval}. We develop a framework for generalized affine phase retrieval with presenting necessary and sufficient conditions for $\\{(M_j,{\\mathbf b}_j)\\}_{j=1}^m$ having generalized affine phase"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07899","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"}