The fundamental limits of stable recovery in compressed sensing
Compressed sensing has shown that a wide variety of structured signals can be recovered from a limited number of noisy linear measurements. This paper considers the extent to which such recovery is robust to signal and measurement uncertainty. The main result is a non-asymptotic upper bound on the reconstruction error in terms of two key quantities: the best approximation error of the signal (with respect to a user-defined approximation set) and the measurement error. We assume a random Gaussian sensing matrix but place no restrictions on the signal or the noise. This result provides a simple and yet powerful framework for analyzing the fundamental limits of stable recovery, allowing us to sharpen existing results as well as derive new ones. © 2014 IEEE.
- Reeves, G
- January 1, 2014
Start / End Page
- 3017 - 3021
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