{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/compressed-sensing-using-generative-models","title":"Compressed Sensing using Generative Models","arxiv_id":"1703.03208","date":"2017-03-09","proceeding":"ICML 2017 8","authors":["Ashish Bora","Ajil Jalal","Eric Price","Alexandros G. Dimakis"],"abstract":"The goal of compressed sensing is to estimate a vector from an\nunderdetermined system of noisy linear measurements, by making use of prior\nknowledge on the structure of vectors in the relevant domain. For almost all\nresults in this literature, the structure is represented by sparsity in a\nwell-chosen basis. We show how to achieve guarantees similar to standard\ncompressed sensing but without employing sparsity at all. Instead, we suppose\nthat vectors lie near the range of a generative model $G: \\mathbb{R}^k \\to\n\\mathbb{R}^n$. Our main theorem is that, if $G$ is $L$-Lipschitz, then roughly\n$O(k \\log L)$ random Gaussian measurements suffice for an $\\ell_2/\\ell_2$\nrecovery guarantee. We demonstrate our results using generative models from\npublished variational autoencoder and generative adversarial networks. Our\nmethod can use $5$-$10$x fewer measurements than Lasso for the same accuracy.","url_abs":"http://arxiv.org/abs/1703.03208v1","url_pdf":"http://arxiv.org/pdf/1703.03208v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"compressed-sensing-using-generative-models","repo_url":"https://github.com/AshishBora/csgm","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"compressed-sensing-using-generative-models","repo_url":"https://github.com/gabsens/Compressed-Sensing-ENSAE","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"compressed-sensing-using-generative-models","repo_url":"https://github.com/giannisdaras/sgilo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1703.03208","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1703.03208"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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