Revisiting the Kronecker Array Transform
It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the senso...
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| Autor*in: |
Masiero, Bruno [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: IEEE signal processing letters - Institute of Electrical and Electronics Engineers ; ID: gnd/1692-5, New York, NY, 19XX, 24(2017), 5, Seite 525-529 |
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| Übergeordnetes Werk: |
volume:24 ; year:2017 ; number:5 ; pages:525-529 |
| Links: |
|---|
| DOI / URN: |
10.1109/LSP.2017.2674969 |
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| 520 | |a It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. | ||
| 650 | 4 | |a Khatri–Rao identity | |
| 650 | 4 | |a Transmission line matrix methods | |
| 650 | 4 | |a Transforms | |
| 650 | 4 | |a Kronecker array transform | |
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| 650 | 4 | |a microphone array | |
| 650 | 4 | |a Acoustics | |
| 650 | 4 | |a Manifolds | |
| 650 | 4 | |a Acoustic arrays | |
| 650 | 4 | |a Microphones | |
| 650 | 4 | |a Fast acoustic imaging | |
| 700 | 1 | |a Nascimento, Vitor H |4 oth | |
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10.1109/LSP.2017.2674969 doi PQ20170901 (DE-627)OLC199340063X (DE-599)GBVOLC199340063X (PRQ)c1061-623545300ad85f92a5528d9dbef181a604f77990b84baad487f138c5f5cf92680 (KEY)02390256u20170000024000500525revisitingthekroneckerarraytransform DE-627 ger DE-627 rakwb eng 53.00 bkl Masiero, Bruno verfasserin aut Revisiting the Kronecker Array Transform 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. Khatri–Rao identity Transmission line matrix methods Transforms Kronecker array transform Sensor arrays microphone array Acoustics Manifolds Acoustic arrays Microphones Fast acoustic imaging Nascimento, Vitor H oth Enthalten in Institute of Electrical and Electronics Engineers ; ID: gnd/1692-5 IEEE signal processing letters New York, NY, 19XX 24(2017), 5, Seite 525-529 (DE-627)182273075 (DE-600)916964-7 1070-9908 nnns volume:24 year:2017 number:5 pages:525-529 http://dx.doi.org/10.1109/LSP.2017.2674969 Volltext http://ieeexplore.ieee.org/document/7864371 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 53.00 AVZ AR 24 2017 5 525-529 |
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10.1109/LSP.2017.2674969 doi PQ20170901 (DE-627)OLC199340063X (DE-599)GBVOLC199340063X (PRQ)c1061-623545300ad85f92a5528d9dbef181a604f77990b84baad487f138c5f5cf92680 (KEY)02390256u20170000024000500525revisitingthekroneckerarraytransform DE-627 ger DE-627 rakwb eng 53.00 bkl Masiero, Bruno verfasserin aut Revisiting the Kronecker Array Transform 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. Khatri–Rao identity Transmission line matrix methods Transforms Kronecker array transform Sensor arrays microphone array Acoustics Manifolds Acoustic arrays Microphones Fast acoustic imaging Nascimento, Vitor H oth Enthalten in Institute of Electrical and Electronics Engineers ; ID: gnd/1692-5 IEEE signal processing letters New York, NY, 19XX 24(2017), 5, Seite 525-529 (DE-627)182273075 (DE-600)916964-7 1070-9908 nnns volume:24 year:2017 number:5 pages:525-529 http://dx.doi.org/10.1109/LSP.2017.2674969 Volltext http://ieeexplore.ieee.org/document/7864371 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 53.00 AVZ AR 24 2017 5 525-529 |
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10.1109/LSP.2017.2674969 doi PQ20170901 (DE-627)OLC199340063X (DE-599)GBVOLC199340063X (PRQ)c1061-623545300ad85f92a5528d9dbef181a604f77990b84baad487f138c5f5cf92680 (KEY)02390256u20170000024000500525revisitingthekroneckerarraytransform DE-627 ger DE-627 rakwb eng 53.00 bkl Masiero, Bruno verfasserin aut Revisiting the Kronecker Array Transform 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. Khatri–Rao identity Transmission line matrix methods Transforms Kronecker array transform Sensor arrays microphone array Acoustics Manifolds Acoustic arrays Microphones Fast acoustic imaging Nascimento, Vitor H oth Enthalten in Institute of Electrical and Electronics Engineers ; ID: gnd/1692-5 IEEE signal processing letters New York, NY, 19XX 24(2017), 5, Seite 525-529 (DE-627)182273075 (DE-600)916964-7 1070-9908 nnns volume:24 year:2017 number:5 pages:525-529 http://dx.doi.org/10.1109/LSP.2017.2674969 Volltext http://ieeexplore.ieee.org/document/7864371 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 53.00 AVZ AR 24 2017 5 525-529 |
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10.1109/LSP.2017.2674969 doi PQ20170901 (DE-627)OLC199340063X (DE-599)GBVOLC199340063X (PRQ)c1061-623545300ad85f92a5528d9dbef181a604f77990b84baad487f138c5f5cf92680 (KEY)02390256u20170000024000500525revisitingthekroneckerarraytransform DE-627 ger DE-627 rakwb eng 53.00 bkl Masiero, Bruno verfasserin aut Revisiting the Kronecker Array Transform 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. Khatri–Rao identity Transmission line matrix methods Transforms Kronecker array transform Sensor arrays microphone array Acoustics Manifolds Acoustic arrays Microphones Fast acoustic imaging Nascimento, Vitor H oth Enthalten in Institute of Electrical and Electronics Engineers ; ID: gnd/1692-5 IEEE signal processing letters New York, NY, 19XX 24(2017), 5, Seite 525-529 (DE-627)182273075 (DE-600)916964-7 1070-9908 nnns volume:24 year:2017 number:5 pages:525-529 http://dx.doi.org/10.1109/LSP.2017.2674969 Volltext http://ieeexplore.ieee.org/document/7864371 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 53.00 AVZ AR 24 2017 5 525-529 |
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Revisiting the Kronecker Array Transform |
| abstract |
It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. |
| abstractGer |
It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. |
| abstract_unstemmed |
It is known that the calculation of a matrix-vector product can be accelerated if this matrix can be recast (or approximated) by the Kronecker product of two smaller matrices. In array signal processing, the manifold matrix can be described as the Kronecker product of two other matrices if the sensor array displays a separable geometry. This forms the basis of the Kronecker Array Transform (KAT), which was previously introduced to speed up the calculations of acoustic images with microphone arrays. If, however, the array has a quasi-separable geometry, e.g., an otherwise separable array with a missing sensor, then the KAT acceleration can no longer be applied. In this letter, we review the definition of the KAT and provide a much simpler derivation that relies on an explicit new relation developed between Kronecker and Khatri-Rao matrix products. Additionally, we extend the KAT to deal with quasi-separable arrays, alleviating the restriction on the need of perfectly separable arrays. |
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| title_short |
Revisiting the Kronecker Array Transform |
| url |
http://dx.doi.org/10.1109/LSP.2017.2674969 http://ieeexplore.ieee.org/document/7864371 |
| remote_bool |
false |
| author2 |
Nascimento, Vitor H |
| author2Str |
Nascimento, Vitor H |
| ppnlink |
182273075 |
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| author2_role |
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| doi_str |
10.1109/LSP.2017.2674969 |
| up_date |
2024-07-03T14:25:56.954Z |
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1803568290943991808 |
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7.4008856 |