Deep Generative Models And Unsupervised Methods For Inverse Problems
Talkat Algorithmic Advances for Statistical Inference with Combinatorial Structure · 2021-10-11..10-15·
summary
Pretrained deep generators serve as differentiable priors to solve ill‑posed inverse problems by optimizing the latent code to match measurements: the CSGM framework uses generators (K≈128–512) mapping to N≈10^6 pixels and guarantees recovery when M ~ K·d·log N under random‑matrix assumptions, while intermediate layer optimization (optimizing early layers of StyleGAN2) reduces artifacts and recovers identities. Empirically this yields up to ~10× fewer measurements than LASSO in some regimes, matches supervised reconstructions in‑distribution, and outperforms them for high‑acceleration MRI on fastMRI. Theory still relies on random weights/expansivity and optimization remains nonconvex.
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chapters (14)
- 0:00Intro
- 4:50Talk Outline
- 10:57Compressed sensing Linear Inverse problems
- 16:41Sparsity in compressed sensing
- 18:02Simplest Inverse problem: Inverting a Generator
- 18:48Inverting a GAN
- 20:50Recovery algorithm: Step 2: Inpainting
- 21:58Recovery algorithm: Step 3: Super-resolution
- 22:44Recovery from linear measurements
- 24:50Theory results
- 32:11Theory for Optimization
- 39:26Comparison to Lasso
- 45:17Conclusions
- 46:20References
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