Wow, the Great Convergence is coming to compressive sensing again !

Compressed Sensing using Generative Models by Ashish Bora, Ajil Jalal, Eric Price, Alexandros G. Dimakis

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(klogL) 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.A tensorflow implementation of "Deep Convolutional Generative Adversarial Networks" is here at: http://carpedm20.github.io/faces/

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