On the sensing matrix performance for support recovery of noisy sparse signals
Lavrenko A, Romer F, Del Galdo G, Thoma RS (2014)
Publication Type: Conference contribution
Publication year: 2014
Publisher: Institute of Electrical and Electronics Engineers Inc.
Pages Range: 679-683
Conference Proceedings Title: 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014
Event location: Atlanta, GA, USA
ISBN: 9781479970889
DOI: 10.1109/GlobalSIP.2014.7032204
Abstract
Recovery of sparse signals from few linear measurements is a central task of the recently emerged area of compressed sensing. Evidently, the design of the measurement plays a key role in the signal recoverability. In this contribution we analyze the explicit dependence between a deterministic sensing matrix and the support recovery performance. We do so by deriving the probability of wrong support recovery and output SNR in the presence of additive input noise. Due to tractability, a closed-form analytical expression can only be found for the 1-sparse case. However, we present numerical evidence that the expressions obtained for 1-sparse case qualitatively capture the trend for the more general iV-sparse case as well. Additionally, the investigations reveal that when designing a measurement, along with the low coherence one has to ensure a stable output SNR. We provide an example of a sensing matrix that, despite having slightly higher coherence, is superior compared to the conventional random matrix with i.i.d. Gaussian entries in terms of the support recovery performance due to providing a constant output SNR.
Involved external institutions
Germany (DE)How to cite
APA:
Lavrenko, A., Romer, F., Del Galdo, G., & Thoma, R.S. (2014). On the sensing matrix performance for support recovery of noisy sparse signals. In 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014 (pp. 679-683). Atlanta, GA, USA: Institute of Electrical and Electronics Engineers Inc..
MLA:
Lavrenko, Anastasia, et al. "On the sensing matrix performance for support recovery of noisy sparse signals." Proceedings of the 2014 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014, Atlanta, GA, USA Institute of Electrical and Electronics Engineers Inc., 2014. 679-683.
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