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Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds

Mota, JFC; Deligiannis, N; Rodrigues, MRD; (2017) Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds. IEEE Transactions on Information Theory , 63 (7) pp. 4472-4496. 10.1109/TIT.2017.2695614. Green open access

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Abstract

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via 1-1 and 1-2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, 1-1 minimization improves the performance of CS dramatically. In contrast, 1-2 minimization has a performance very similar to classical CS, and brings no significant benefits. In addition, we use the insight provided by our bounds to design practical schemes to improve prior information. All our findings are illustrated with experimental results.

Type: Article
Title: Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds
Location: Atlanta, GA
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/TIT.2017.2695614
Publisher version: http://doi.org/10.1109/TIT.2017.2695614
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/
Keywords: Science & Technology, Technology, Computer Science, Information Systems, Engineering, Electrical & Electronic, Computer Science, Engineering, Compressed sensing, prior information, basis pursuit, l(1)-l(1) and l(1)-l(2) minimization, Gaussian width, RESTRICTED ISOMETRY PROPERTY, RECONSTRUCTION, MATRICES, SIGNALS, MRI
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1561644
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