Signal Recovery With Generative Priors

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" summary

Random ReLU feedforward generators with Gaussian weights and expansive layers are modeled as the prior and shown to permit compressive phase retrieval from phaseless linear measurements with optimal sample complexity ~k (ignoring logs) when the measurement matrix is Gaussian and the network is given. The nonconvex loss has a benign landscape so gradient descent converges (with a minor tweak) and experiments on digits beat sparsity methods at low measurements, but representation error causes an empirical error floor and out‑of‑distribution failures.

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" chapters (14)

1. 0:00Intro
2. 2:03Recovery Guarantee for Sparse Signals
3. 2:54Sparsity appears to fail in Compressive Phase Retrieval
4. 5:44With generic measurements, Sparse PhaseLift gives suboptimal sample complexity
5. 7:42Deep Generative Models
6. 8:37Visualization of a generative model and its latent space
7. 10:45Compressed Sensing with Generative Models
8. 12:29Geometric picture of signal recovery with a low-dimensional generative prior
9. 14:56Random generative priors allow rigorous recovery guarantees
10. 17:54Compressive phase retrieval from generic measurements is possible at optimal sample complexity
11. 21:27Proof requires concentration of discontinuous matrix- valued random functions
12. 23:23Deep phase retrieval can outperform sparse phase retrieval in the low measurement regime
13. 26:33Signal Recovery Under Generative Priors
14. 28:59References

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