A new family of low coherence finite Gabor frames and applications in compressive sampling

Alihan Kaplan; Volker Pohl; Holger Boche

doi:10.1109/SPAWC.2019.8815438

A new family of low coherence finite Gabor frames and applications in compressive sampling

Alihan Kaplan, Volker Pohl, Holger Boche

Chair of Theoretical Information Technology

Technical University of Munich

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Gabor frames with low coherence are applied in diverse engineering theoretic frameworks such as CDMA, discrete radar, or for the measuremet of time-vayring channels. This paper proposes a construction of a new family of low coherence finite Gabor frames in dimensions pn^-1 where p is a prime number and n is a positive integer. For these dimensions, similar constructions were previously not known. It is shown that these frames are close to maximally equiangular frames, i.e. the coherence of these frames is close to the Welch bound. Additionally some results on statistical sparse vector recovery are proven for the proposed Gabor frames, verifying their suitability as sensing matrices in compressive sampling.

Original language	English
Title of host publication	2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781538665282
DOIs	https://doi.org/10.1109/SPAWC.2019.8815438
State	Published - Jul 2019
Event	20th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019 - Cannes, France Duration: 2 Jul 2019 → 5 Jul 2019

Publication series

Name	IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC
Volume	2019-July

Conference

Conference	20th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019
Country/Territory	France
City	Cannes
Period	2/07/19 → 5/07/19

Keywords

deterministic compressive sampling
finite Gabor frames
low coherence frames
statistical RIP
strong coherence property

Access to Document

10.1109/SPAWC.2019.8815438

Cite this

Kaplan, A., Pohl, V., & Boche, H. (2019). A new family of low coherence finite Gabor frames and applications in compressive sampling. In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019 Article 8815438 (IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SPAWC.2019.8815438

Kaplan, Alihan ; Pohl, Volker ; Boche, Holger. / A new family of low coherence finite Gabor frames and applications in compressive sampling. 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. (IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC).

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abstract = "Gabor frames with low coherence are applied in diverse engineering theoretic frameworks such as CDMA, discrete radar, or for the measuremet of time-vayring channels. This paper proposes a construction of a new family of low coherence finite Gabor frames in dimensions pn-1 where p is a prime number and n is a positive integer. For these dimensions, similar constructions were previously not known. It is shown that these frames are close to maximally equiangular frames, i.e. the coherence of these frames is close to the Welch bound. Additionally some results on statistical sparse vector recovery are proven for the proposed Gabor frames, verifying their suitability as sensing matrices in compressive sampling.",

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Kaplan, A, Pohl, V & Boche, H 2019, A new family of low coherence finite Gabor frames and applications in compressive sampling. in 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019., 8815438, IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., 20th IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019, Cannes, France, 2/07/19. https://doi.org/10.1109/SPAWC.2019.8815438

A new family of low coherence finite Gabor frames and applications in compressive sampling. / Kaplan, Alihan; Pohl, Volker; Boche, Holger.
2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8815438 (IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Gabor frames with low coherence are applied in diverse engineering theoretic frameworks such as CDMA, discrete radar, or for the measuremet of time-vayring channels. This paper proposes a construction of a new family of low coherence finite Gabor frames in dimensions pn-1 where p is a prime number and n is a positive integer. For these dimensions, similar constructions were previously not known. It is shown that these frames are close to maximally equiangular frames, i.e. the coherence of these frames is close to the Welch bound. Additionally some results on statistical sparse vector recovery are proven for the proposed Gabor frames, verifying their suitability as sensing matrices in compressive sampling.

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Kaplan A, Pohl V, Boche H. A new family of low coherence finite Gabor frames and applications in compressive sampling. In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications, SPAWC 2019. Institute of Electrical and Electronics Engineers Inc. 2019. 8815438. (IEEE Workshop on Signal Processing Advances in Wireless Communications, SPAWC). doi: 10.1109/SPAWC.2019.8815438

A new family of low coherence finite Gabor frames and applications in compressive sampling

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