{"paper":{"title":"Fast Algorithms for Demixing Sparse Signals from Nonlinear Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Chinmay Hegde, Mohammadreza Soltani","submitted_at":"2016-08-03T16:03:25Z","abstract_excerpt":"We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \\ i=1,\\ldots,m$, where $x = \\Phi w+\\Psi z$ denotes the superposition signal, $\\Phi$ and $\\Psi$ are orthonormal bases in $\\mathbb{R}^n$, and $w, z\\in\\mathbb{R}^n$ are sparse coefficient vectors of the constituent signals, and $e_i$ represents the noise. Moreover, $g$ represents a nonlinear link function, and $a_i\\in\\mathbb{R}^n$ is the $i$-th row of the measurement matrix, $A\\in\\mathbb{R}^{m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01234","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"}