Compressed Sensing with Rank Deficient Dictionaries

Thomas Lundgaard Hansen; Daniel Højrup Johansen; Peter Bjørn Jørgensen; Kasper Fløe Trillingsgard; Thomas Arildsen; Karsten Fyhn; Torben Larsen

doi:10.1109/GLOCOM.2012.6503673

Compressed Sensing with Rank Deficient Dictionaries

Thomas Lundgaard Hansen, Daniel Højrup Johansen, Peter Bjørn Jørgensen, Kasper Fløe Trillingsgard, Thomas Arildsen, Karsten Fyhn, Torben Larsen

Department of Electronic Systems

Research output: Contribution to journal › Conference article in Journal › Research › peer-review

3 Citations (Scopus)

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Abstract

In compressed sensing it is generally assumed that the dictionary matrix constitutes a (possibly overcomplete) basis of the signal space. In this paper we consider dictionaries that do not span the signal space, i.e. rank deficient dictionaries. We show that in this case the signal-to-noise ratio (SNR) in the compressed samples can be increased by selecting the rows of the measurement matrix from the column space of the dictionary. As an example application of compressed sensing with a rank deficient dictionary, we present a case study of compressed sensing applied to the Coarse Acquisition (C/A) step in a GPS receiver. Simulations show that for this application the
proposed choice of measurement matrix yields an increase in SNR performance of up to 5 − 10 dB, compared to the conventional choice of a fully random measurement matrix. Furthermore, the compressed sensing based C/A step is compared to a conventional method for GPS C/A.

Original language	English
Journal	Globecom. I E E E Conference and Exhibition
Pages (from-to)	3594-3599
Number of pages	6
ISSN	1930-529X
DOIs	https://doi.org/10.1109/GLOCOM.2012.6503673
Publication status	Published - 2012
Event	IEEE Globecom 2012: Globecom Communications Conference - Disneyland Hotel, Anaheim, California, United States Duration: 3 Dec 2012 → 7 Dec 2012

Conference

Conference	IEEE Globecom 2012
Location	Disneyland Hotel
Country/Territory	United States
City	Anaheim, California
Period	03/12/2012 → 07/12/2012

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10.1109/GLOCOM.2012.6503673

Compressed Sensing with Rank Deficient Dictionaries_Globecom12Accepted author manuscript, 507 KB

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Cite this

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title = "Compressed Sensing with Rank Deficient Dictionaries",

abstract = "In compressed sensing it is generally assumed that the dictionary matrix constitutes a (possibly overcomplete) basis of the signal space. In this paper we consider dictionaries that do not span the signal space, i.e. rank deficient dictionaries. We show that in this case the signal-to-noise ratio (SNR) in the compressed samples can be increased by selecting the rows of the measurement matrix from the column space of the dictionary. As an example application of compressed sensing with a rank deficient dictionary, we present a case study of compressed sensing applied to the Coarse Acquisition (C/A) step in a GPS receiver. Simulations show that for this application theproposed choice of measurement matrix yields an increase in SNR performance of up to 5 − 10 dB, compared to the conventional choice of a fully random measurement matrix. Furthermore, the compressed sensing based C/A step is compared to a conventional method for GPS C/A.",

author = "Hansen, {Thomas Lundgaard} and Johansen, {Daniel H{\o}jrup} and J{\o}rgensen, {Peter Bj{\o}rn} and Trillingsgard, {Kasper Fl{\o}e} and Thomas Arildsen and Karsten Fyhn and Torben Larsen",

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AU - Johansen, Daniel Højrup

AU - Jørgensen, Peter Bjørn

AU - Trillingsgard, Kasper Fløe

AU - Arildsen, Thomas

AU - Fyhn, Karsten

AU - Larsen, Torben

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AB - In compressed sensing it is generally assumed that the dictionary matrix constitutes a (possibly overcomplete) basis of the signal space. In this paper we consider dictionaries that do not span the signal space, i.e. rank deficient dictionaries. We show that in this case the signal-to-noise ratio (SNR) in the compressed samples can be increased by selecting the rows of the measurement matrix from the column space of the dictionary. As an example application of compressed sensing with a rank deficient dictionary, we present a case study of compressed sensing applied to the Coarse Acquisition (C/A) step in a GPS receiver. Simulations show that for this application theproposed choice of measurement matrix yields an increase in SNR performance of up to 5 − 10 dB, compared to the conventional choice of a fully random measurement matrix. Furthermore, the compressed sensing based C/A step is compared to a conventional method for GPS C/A.

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Compressed Sensing with Rank Deficient Dictionaries

Abstract

Conference

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AUB Link

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PhD project: Compressive Sensing in Communication Systems

SparSig: Sparse Signal Processing in Wireless Communications

Cite this

Compressed Sensing with Rank Deficient Dictionaries

Abstract

Conference

Access to Document

AUB Link

Other files and links

Fingerprint

Projects

PhD project: Compressive Sensing in Communication Systems

SparSig: Sparse Signal Processing in Wireless Communications

Cite this