# Global Guarantees for Blind Demodulation with Generative Priors

arXiv: https://arxiv.org/abs/1905.12576 · HTML: https://mlsanity.com/paper/1905.12576/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 11 of 11)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Instance-Optimal Compressed Sensing via Posterior Sampling](https://mlsanity.com/paper/2106.11438/) (2021)
- [Quantized Compressed Sensing with Score-based Generative Models](https://mlsanity.com/paper/2211.13006/) (2022)
- [A coherence parameter characterizing generative compressed sensing with Fourier measurements](https://mlsanity.com/paper/2207.09340/) (2022)
- [Med-Real2Sim: Non-Invasive Medical Digital Twins using Physics-Informed Self-Supervised Learning](https://mlsanity.com/paper/2403.00177/) (2024)
- [Robust 1-bit Compressive Sensing with Partial Gaussian Circulant Matrices and Generative Priors](https://mlsanity.com/paper/2108.03570/) (2021)
- [QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models](https://mlsanity.com/paper/2302.00919/) (2023)
- [Signal Recovery with Non-Expansive Generative Network Priors](https://mlsanity.com/paper/2204.13599/) (2022)
- [Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems](https://mlsanity.com/paper/2603.07357/) (2026)
- [Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regime](https://mlsanity.com/paper/2411.18189/) (2024)

## Abstract (arXiv)

We study a deep learning inspired formulation for the blind demodulation problem, which is the task of recovering two unknown vectors from their entrywise multiplication. We consider the case where the unknown vectors are in the range of known deep generative models, G(1):ℝnrightarrowℝℓ and G(2):ℝprightarrowℝℓ. In the case when the networks corresponding to the generative models are expansive, the weight matrices are random and the dimension of the unknown vectors satisfy ℓ = Omega(n2+p2), up to log factors, we show that the empirical risk objective has a favorable landscape for optimization. That is, the objective function has a descent direction at every point outside of a small neighborhood around four hyperbolic curves. We also characterize the local maximizers of the empirical risk objective and, hence, show that there does not exist any other stationary points outside of these neighborhood around four hyperbolic curves and the set of local maximizers. We also implement a gradient descent scheme inspired by the geometry of the landscape of the objective function. In order to converge to a global minimizer, this gradient descent scheme exploits the fact that exactly one of the hyperbolic curve corresponds to the global minimizer, and thus points near this hyperbolic curve have a lower objective value than points close to the other spurious hyperbolic curves. We show that this gradient descent scheme can effectively remove distortions synthetically introduced to the MNIST dataset.