mlsanityData to 7 Oct 2026

Compressed Sensing using Generative Models

arXiv 1703.03208 ↗First posted 9 Mar 2017stat.ML cs.IT cs.LGcited by 337

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Cited by 83 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

The goal of compressed sensing is to estimate a vector from an underdetermined system of noisy linear measurements, by making use of prior knowledge on the structure of vectors in the relevant domain. For almost all results in this literature, the structure is represented by sparsity in a well-chosen basis. We show how to achieve guarantees similar to standard compressed sensing but without employing sparsity at all. Instead, we suppose that vectors lie near the range of a generative model G: ℝk → ℝn. Our main theorem is that, if G is L-Lipschitz, then roughly O(k log L) random Gaussian measurements suffice for an ℓ2/ℓ2 recovery guarantee. We demonstrate our results using generative models from published variational autoencoder and generative adversarial networks. Our method can use 5-10x fewer measurements than Lasso for the same accuracy.

Key facts. Cited by 337 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Mar 2017.

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Citing papers per year: 2021: 60; 2022: 70; 2023: 68; 2024: 46; 2025: 51; 2026: 42.

337 papers.

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