Compressed Sensing with Rank Deficient Dictionaries

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

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2 Citationer (Scopus)
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Resumé

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.
OriginalsprogEngelsk
TidsskriftGlobecom. I E E E Conference and Exhibition
Sider (fra-til)3594-3599
Antal sider6
ISSN1930-529X
DOI
StatusUdgivet - 2012
BegivenhedIEEE Globecom 2012: Globecom Communications Conference - Disneyland Hotel, Anaheim, California, USA
Varighed: 3 dec. 20127 dec. 2012

Konference

KonferenceIEEE Globecom 2012
LokationDisneyland Hotel
LandUSA
ByAnaheim, California
Periode03/12/201207/12/2012

Fingerprint

Compressed sensing
Glossaries
Global positioning system
Signal to noise ratio

Citer dette

Hansen, Thomas Lundgaard ; Johansen, Daniel Højrup ; Jørgensen, Peter Bjørn ; Trillingsgard, Kasper Fløe ; Arildsen, Thomas ; Fyhn, Karsten ; Larsen, Torben. / Compressed Sensing with Rank Deficient Dictionaries. I: Globecom. I E E E Conference and Exhibition. 2012 ; s. 3594-3599.
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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.",
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Compressed Sensing with Rank Deficient Dictionaries. / Hansen, Thomas Lundgaard; Johansen, Daniel Højrup; Jørgensen, Peter Bjørn; Trillingsgard, Kasper Fløe; Arildsen, Thomas; Fyhn, Karsten; Larsen, Torben.

I: Globecom. I E E E Conference and Exhibition, 2012, s. 3594-3599.

Publikation: Bidrag til tidsskriftKonferenceartikel i tidsskriftForskningpeer review

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AU - Jørgensen, Peter Bjørn

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AU - Arildsen, Thomas

AU - Fyhn, Karsten

AU - Larsen, Torben

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