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We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements and \emph{any} prior distribution on the signal, that the conditional resampling estimator achieves near-optimal recovery guarantees. Moreover, this result is robust to model mismatch, as long as the distribution estimate (e.g., from an invertible generative model) is close to the true distribution in Wasserstein distance. We implement the conditional resampling estimator for deep generative priors using Langevin dynamics, and empirically find that it produces accurate estimates with more diversity than MAP.
Author Information
Ajil Jalal (University of Texas at Austin)
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2021 Poster: Robust Compressed Sensing MRI with Deep Generative Priors »
Ajil Jalal · Marius Arvinte · Giannis Daras · Eric Price · Alex Dimakis · Jon Tamir -
2020 Poster: Robust compressed sensing using generative models »
Ajil Jalal · Liu Liu · Alex Dimakis · Constantine Caramanis -
2019 Poster: Inverting Deep Generative models, One layer at a time »
Qi Lei · Ajil Jalal · Inderjit Dhillon · Alex Dimakis -
2018 : Poster session »
David Zeng · Marzieh S. Tahaei · Shuai Chen · Felix Meister · Meet Shah · Anant Gupta · Ajil Jalal · Eirini Arvaniti · David Zimmerer · Konstantinos Kamnitsas · Pedro Ballester · Nathaniel Braman · Udaya Kumar · Sil C. van de Leemput · Junaid Qadir · Hoel Kervadec · Mohamed Akrout · Adrian Tousignant · Matthew Ng · Raghav Mehta · Miguel Monteiro · Sumana Basu · Jonas Adler · Adrian Dalca · Jizong Peng · Sungyeob Han · Xiaoxiao Li · Karthik Gopinath · Joseph Cheng · Bogdan Georgescu · Kha Gia Quach · Karthik Sarma · David Van Veen -
2018 : Oral session I »
Jonas Adler · Ajil Jalal · Joseph Cheng