Compressed Sensing using Generative Models

Ashish Bora, Ajil Jalal, Eric Price, Alexandros G. Dimakis
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:537-546, 2017.

Abstract

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 $G: \mathbb{R}^k \to \mathbb{R}^n$. Our main theorem is that, if $G$ is $L$-Lipschitz, then roughly $\mathcal{O}(k \log L)$ random Gaussian measurements suffice for an $\ell_2/\ell_2$ recovery guarantee. We demonstrate our results using generative models from published variational autoencoder and generative adversarial networks. Our method can use $5$-$10$x fewer measurements than Lasso for the same accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-bora17a, title = {Compressed Sensing using Generative Models}, author = {Ashish Bora and Ajil Jalal and Eric Price and Alexandros G. Dimakis}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {537--546}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/bora17a/bora17a.pdf}, url = {https://proceedings.mlr.press/v70/bora17a.html}, abstract = {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 $G: \mathbb{R}^k \to \mathbb{R}^n$. Our main theorem is that, if $G$ is $L$-Lipschitz, then roughly $\mathcal{O}(k \log L)$ random Gaussian measurements suffice for an $\ell_2/\ell_2$ recovery guarantee. We demonstrate our results using generative models from published variational autoencoder and generative adversarial networks. Our method can use $5$-$10$x fewer measurements than Lasso for the same accuracy.} }
Endnote
%0 Conference Paper %T Compressed Sensing using Generative Models %A Ashish Bora %A Ajil Jalal %A Eric Price %A Alexandros G. Dimakis %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-bora17a %I PMLR %P 537--546 %U https://proceedings.mlr.press/v70/bora17a.html %V 70 %X 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 $G: \mathbb{R}^k \to \mathbb{R}^n$. Our main theorem is that, if $G$ is $L$-Lipschitz, then roughly $\mathcal{O}(k \log L)$ random Gaussian measurements suffice for an $\ell_2/\ell_2$ recovery guarantee. We demonstrate our results using generative models from published variational autoencoder and generative adversarial networks. Our method can use $5$-$10$x fewer measurements than Lasso for the same accuracy.
APA
Bora, A., Jalal, A., Price, E. & Dimakis, A.G.. (2017). Compressed Sensing using Generative Models. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:537-546 Available from https://proceedings.mlr.press/v70/bora17a.html.

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