Robust Compressed Sensing using Generative Models

Understand

The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations.

• In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume the vector is represented by a deep generative model $G: \mathbb{R}^k \rightarrow \mathbb{R}^n$.
• Classical recovery approaches such as empirical risk minimization (ERM) are guaranteed to succeed when the measurement matrix is sub-Gaussian.
• However, when the measurement matrix and measurements are heavy-tailed or have outliers, recovery may fail dramatically.