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A domain-specific generative model can provide a stronger\nprior and thus allow for recovery with far fewer measurements. However, unlike\nsparsity-based approaches, existing methods based on generative models\nguarantee exact recovery only over their support, which is typically only a\nsmall subset of the space on which the signals are defined. We propose\nSparse-Gen, a framework that allows for sparse deviations from the support set,\nthereby achieving the best of both worlds by using a domain specific prior and\nallowing reconstruction over the full space of signals. Theoretically, our\nframework provides a new class of signals that can be acquired using compressed\nsensing, reducing classic sparse vector recovery to a special case and avoiding\nthe restrictive support due to a generative model prior. Empirically, we\nobserve consistent improvements in reconstruction accuracy over competing\napproaches, especially in the more practical setting of transfer compressed\nsensing where a generative model for a data-rich, source domain aids sensing on\na data-scarce, target domain.","url_abs":"http://arxiv.org/abs/1807.01442v2","url_pdf":"http://arxiv.org/pdf/1807.01442v2.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":"modeling-sparse-deviations-for-compressed","repo_url":"https://github.com/aditya-grover/uae","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"modeling-sparse-deviations-for-compressed","repo_url":"https://github.com/ermongroup/sparse_gen","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"compressed-sensing","task_name":"compressed sensing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.01442","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1807.01442"}},"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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