Provable Compressed Sensing with Generative Priors via Langevin Dynamics

02/25/2021
by   Thanh V. Nguyen, et al.
0

Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. Here, we assume an unknown signal to lie in the range of some pre-trained generative model. A popular approach for signal recovery is via gradient descent in the low-dimensional latent space. While gradient descent has achieved good empirical performance, its theoretical behavior is not well understood. In this paper, we introduce the use of stochastic gradient Langevin dynamics (SGLD) for compressed sensing with a generative prior. Under mild assumptions on the generative model, we prove the convergence of SGLD to the true signal. We also demonstrate competitive empirical performance to standard gradient descent.

READ FULL TEXT

page 12

page 13

research
06/28/2022

Equivariant Priors for Compressed Sensing with Unknown Orientation

In compressed sensing, the goal is to reconstruct the signal from an und...
research
02/22/2021

Generator Surgery for Compressed Sensing

Image recovery from compressive measurements requires a signal prior for...
research
06/20/2021

Generative Model Adversarial Training for Deep Compressed Sensing

Deep compressed sensing assumes the data has sparse representation in a ...
research
06/21/2021

Instance-Optimal Compressed Sensing via Posterior Sampling

We characterize the measurement complexity of compressed sensing of sign...
research
09/02/2021

Solving Inverse Problems with Conditional-GAN Prior via Fast Network-Projected Gradient Descent

The projected gradient descent (PGD) method has shown to be effective in...
research
01/15/2019

Using auto-encoders for solving ill-posed linear inverse problems

Compressed sensing algorithms recover a signal from its under-determined...
research
03/25/2018

SUNLayer: Stable denoising with generative networks

It has been experimentally established that deep neural networks can be ...

Please sign up or login with your details

Forgot password? Click here to reset