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A Unified Approach to Uniform Signal Recovery From Non-Linear Observations by Genzel, Martin; Stollenwerk, Alexander is a scholarly article available to read on EtoBox.

What is A Unified Approach to Uniform Signal Recovery From Non-Linear Observations about?

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated guarantees is uniformity, i.e., recovery succeeds for an entire class of structured signals with a fixed measurement ensemble. However, despite significant results in various special cases, a general understanding of uniform recovery from non-linear observations is still missing. This paper develops a unified approach to this problem under the assumption of i.i.d. sub-Gaussian measurement vectors. Our main result shows that a simple least-squares estimator with any convex constraint can serve as a universal recovery strategy, which is outlier robust and does not require explicit knowledge of the underlying non-linearity. Based on empirical process theory, a key technical novelty is an approximative increment condition that can be implemented for all common types of non-linear models. This flexibility allows us to apply our approach to a variety of problems in non-linear compressed sensing and high-dimensional statistics, leading to several new and imp

Author

Genzel, Martin; Stollenwerk, Alexander

Published

2020

Language

EN