Surpassing the Theoretical 1-Norm Phase Transition in Compressive Sensing by Tuning the Smoothed L0 Algorithm

Christian Schou Oxvig, Patrick Steffen Pedersen, Thomas Arildsen, Torben Larsen

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Resumé

Reconstruction of an undersampled signal is at the root of compressive sensing: when is an algorithm capable of reconstructing the signal? what quality is achievable? and how much time does reconstruction require? We have considered the worst-case performance of the smoothed ℓ0 norm reconstruction algorithm in a noiseless setup. Through an empirical tuning of its parameters, we have improved the phase transition (capabilities) of the algorithm for fixed quality and required time. In this paper, we present simulation results that show a phase transition surpassing that of the theoretical ℓ1 approach: the proposed modified algorithm obtains 1-norm phase transition with greatly reduced required computation time.

OriginalsprogEngelsk
TitelAcoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on
ForlagIEEE
Publikationsdato2013
Sider6019-6023
ISBN (Trykt)978-1-4799-0356-6
DOI
StatusUdgivet - 2013
Begivenhed2013 IEEE International Conference on Acoustics, Speech, and Signal Processing - Vancouver, Canada
Varighed: 26 maj 201331 maj 2013
Konferencens nummer: 38

Konference

Konference2013 IEEE International Conference on Acoustics, Speech, and Signal Processing
Nummer38
LandCanada
ByVancouver
Periode26/05/201331/05/2013
NavnI E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings
ISSN1520-6149

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Oxvig, C. S., Pedersen, P. S., Arildsen, T., & Larsen, T. (2013). Surpassing the Theoretical 1-Norm Phase Transition in Compressive Sensing by Tuning the Smoothed L0 Algorithm. I Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on (s. 6019-6023). IEEE. I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings https://doi.org/10.1109/ICASSP.2013.6638820
Oxvig, Christian Schou ; Pedersen, Patrick Steffen ; Arildsen, Thomas ; Larsen, Torben. / Surpassing the Theoretical 1-Norm Phase Transition in Compressive Sensing by Tuning the Smoothed L0 Algorithm. Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on . IEEE, 2013. s. 6019-6023 (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings).
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Oxvig, CS, Pedersen, PS, Arildsen, T & Larsen, T 2013, Surpassing the Theoretical 1-Norm Phase Transition in Compressive Sensing by Tuning the Smoothed L0 Algorithm. i Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on . IEEE, I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings, s. 6019-6023, Vancouver, Canada, 26/05/2013. https://doi.org/10.1109/ICASSP.2013.6638820

Surpassing the Theoretical 1-Norm Phase Transition in Compressive Sensing by Tuning the Smoothed L0 Algorithm. / Oxvig, Christian Schou; Pedersen, Patrick Steffen; Arildsen, Thomas; Larsen, Torben.

Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on . IEEE, 2013. s. 6019-6023.

Publikation: Bidrag til bog/antologi/rapport/konference proceedingKonferenceartikel i proceedingForskningpeer review

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AU - Oxvig, Christian Schou

AU - Pedersen, Patrick Steffen

AU - Arildsen, Thomas

AU - Larsen, Torben

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N2 - Reconstruction of an undersampled signal is at the root of compressive sensing: when is an algorithm capable of reconstructing the signal? what quality is achievable? and how much time does reconstruction require? We have considered the worst-case performance of the smoothed ℓ0 norm reconstruction algorithm in a noiseless setup. Through an empirical tuning of its parameters, we have improved the phase transition (capabilities) of the algorithm for fixed quality and required time. In this paper, we present simulation results that show a phase transition surpassing that of the theoretical ℓ1 approach: the proposed modified algorithm obtains 1-norm phase transition with greatly reduced required computation time.

AB - Reconstruction of an undersampled signal is at the root of compressive sensing: when is an algorithm capable of reconstructing the signal? what quality is achievable? and how much time does reconstruction require? We have considered the worst-case performance of the smoothed ℓ0 norm reconstruction algorithm in a noiseless setup. Through an empirical tuning of its parameters, we have improved the phase transition (capabilities) of the algorithm for fixed quality and required time. In this paper, we present simulation results that show a phase transition surpassing that of the theoretical ℓ1 approach: the proposed modified algorithm obtains 1-norm phase transition with greatly reduced required computation time.

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Oxvig CS, Pedersen PS, Arildsen T, Larsen T. Surpassing the Theoretical 1-Norm Phase Transition in Compressive Sensing by Tuning the Smoothed L0 Algorithm. I Acoustics, Speech and Signal Processing (ICASSP), 2013 IEEE International Conference on . IEEE. 2013. s. 6019-6023. (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings). https://doi.org/10.1109/ICASSP.2013.6638820