Can compressed sensing beat the Nyquist sampling rate?

TL;DR

This paper critically examines the claims of compressed sensing surpassing Nyquist sampling, demonstrating that in realistic scenarios, it offers less data saving than theoretically expected and clarifies common misconceptions.

Contribution

The paper clarifies misconceptions about compressed sensing's ability to beat Nyquist sampling and shows it provides less data saving than theoretical bounds in practical scenarios.

Findings

Compressed sensing's data saving is below theoretical upper bounds.

In realistic scenarios, compressed sensing offers less advantage than claimed.

Misinterpretations in literature about beating Nyquist are clarified.

Abstract

Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that, in a realistic scenario for signals that are believed to be sparse, one can achieve a substantially larger saving than compressing sensing can. It is also shown that frequent assertions in the literature that "Compressed sensing" can beat the Nyquist sampling approach are misleading substitution of terms and are rooted in misinterpretation of the sampling theory.