{"paper":{"title":"Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Arian Maleki, Ji Xu, Junjie Ma","submitted_at":"2021-11-05T03:18:50Z","abstract_excerpt":"We consider an inverse problem $\\mathbf{y}= f(\\mathbf{Ax})$, where $\\mathbf{x}\\in\\mathbb{R}^n$ is the signal of interest, $\\mathbf{A}$ is the sensing matrix, $f$ is a nonlinear function and $\\mathbf{y} \\in \\mathbb{R}^m$ is the measurement vector. In many applications, we have some level of freedom to design the sensing matrix $\\mathbf{A}$, and in such circumstances we could optimize $\\mathbf{A}$ to achieve better reconstruction performance. As a first step towards optimal design, it is important to understand the impact of the sensing matrix on the difficulty of recovering $\\mathbf{x}$ from $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.03237","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.03237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}