Recovery error bounds on compressed sensing of noisy signals

Abstract

Compressed sensing is an emerging technique in the field of digital signal acquisition. It promises almost exact recovery of high-dimensional signals from a very small set of measurements. However, this technique is challenged by the task of recovering signals immersed in noise. In this paper, we derive upper and lower bounds on mean squared recovery error of noisy signals. These bounds are valid for any number of acquired measurements and at any signal-to-noise ratio. This work is highly useful for the design of any compressed sensing-based real world application by quantifying recovery error entailed with realistic digital signal acquisition scenarios.