We address the problem of compressed sensing (CS)with prior information: reconstruct a target CS signal with theaid of a similar signal that is known beforehand, our priorinformation. We integrate the additional knowledge of the similarsignal into CS via â„“1-â„“1 and â„“1-â„“2 minimization. We thenestablish bounds on the number of measurements required bythese problems to successfully reconstruct the original signal.Our bounds and geometrical interpretations reveal that if theprior information has good enough quality, â„“1-â„“1 minimizationimproves the performance of CS dramatically. In contrast, â„“1-â„“2 minimization has a performance very similar to classicalCS and brings no significant benefits. In addition, we use theinsight provided by our bounds to design practical schemes toimprove prior information. All our findings are illustrated withexperimental results.
Mota, J, Deligiannis, N & Rodrigues, M 2017, 'Compressed sensing with prior Information: Strategies, geometry, and bounds', IEEE Transactions on Information Theory, vol. 63, no. 7, 7904593, pp. 4472-4496. https://doi.org/10.1109/TIT.2017.2695614
Mota, J., Deligiannis, N., & Rodrigues, M. (2017). Compressed sensing with prior Information: Strategies, geometry, and bounds. IEEE Transactions on Information Theory, 63(7), 4472-4496. Article 7904593. https://doi.org/10.1109/TIT.2017.2695614
@article{2e9d9cb63b4e4d4d9684c35db4ae9f52,
title = "Compressed sensing with prior Information: Strategies, geometry, and bounds",
abstract = "We address the problem of compressed sensing (CS)with prior information: reconstruct a target CS signal with theaid of a similar signal that is known beforehand, our priorinformation. We integrate the additional knowledge of the similarsignal into CS via â„“1-â„“1 and â„“1-â„“2 minimization. We thenestablish bounds on the number of measurements required bythese problems to successfully reconstruct the original signal.Our bounds and geometrical interpretations reveal that if theprior information has good enough quality, â„“1-â„“1 minimizationimproves the performance of CS dramatically. In contrast, â„“1-â„“2 minimization has a performance very similar to classicalCS and brings no significant benefits. In addition, we use theinsight provided by our bounds to design practical schemes toimprove prior information. All our findings are illustrated withexperimental results.",
keywords = "Compressed sensing, Gaussian width., basis pursuit, prior information, â„“ -â„“ and â„“ -â„“ minimization",
author = "Joao Mota and Nikolaos Deligiannis and Miguel Rodrigues",
year = "2017",
month = jul,
doi = "10.1109/TIT.2017.2695614",
language = "English",
volume = "63",
pages = "4472--4496",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "7",
}