Compact order polynomial singular value decomposition of a matrix of analytic functions

Mohammed A. Bakhit; Faizan A. Khattak; Ian K. Proudler; Stephan Weiss; Garrey W. Rice

doi:10.1109/CAMSAP58249.2023.10403445

Compact order polynomial singular value decomposition of a matrix of analytic functions

Mohammed A. Bakhit, Faizan A. Khattak, Ian K. Proudler, Stephan Weiss, Garrey W. Rice

Electronic And Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

3 Citations (Scopus)

42 Downloads (Pure)

Abstract

This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD for analytic, non-multiplexed polynomial matrices. The proposed method calculates a conventional SVD in sample points on the unit circle, and then applies phase smoothing algorithms to establish phase-coherence between adjacent frequency bins. This results in the extraction of compact order singular values and their corresponding singular vectors. The method is evaluated through experiments conducted on an ensemble of randomised polynomial matrices, demonstrating its superior performance in terms of higher decomposition accuracy and lower polynomial order compared to state-of-the-art techniques.

Original language	English
Title of host publication	2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	416-420
Number of pages	5
ISBN (Electronic)	9798350344523
DOIs	https://doi.org/10.1109/CAMSAP58249.2023.10403445
Publication status	Published - 31 Jan 2024
Event	9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing - Los Suenos, Costa Rica Duration: 10 Dec 2023 → 13 Dec 2023 https://camsap23.ig.umons.ac.be/

Workshop

Workshop	9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
Abbreviated title	CAMSAP
Country/Territory	Costa Rica
City	Los Suenos
Period	10/12/23 → 13/12/23
Internet address	https://camsap23.ig.umons.ac.be/

Keywords

singular value decomposition
polynomial matrices
decomposition

Access to Document

10.1109/CAMSAP58249.2023.10403445

Bakhit-etal-CAMSAP-2023-Compact-order-polynomial-singular-value-decompositionAccepted author manuscript, 662 KBLicence: Strath_1

1 Finished

Signal Processing in the Information Age (UDRC III)
Weiss, S. (Principal Investigator) & Stankovic, V. (Co-investigator)
EPSRC (Engineering and Physical Sciences Research Council)
1/07/18 → 31/03/24
Project: Research

3 Citations
1 Article

On properties and structure of the analytic singular value decomposition
Weiss, S., Proudler, I. K., Barbarino, G., Pestana, J. & McWhirter, J. G., 8 May 2024, In: IEEE Transactions on Signal Processing. 72, p. 2260-2275 16 p.
Research output: Contribution to journal › Article › peer-review

Open Access
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7 Citations (Scopus)

172 Downloads (Pure)

Cite this

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title = "Compact order polynomial singular value decomposition of a matrix of analytic functions",

abstract = "This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD for analytic, non-multiplexed polynomial matrices. The proposed method calculates a conventional SVD in sample points on the unit circle, and then applies phase smoothing algorithms to establish phase-coherence between adjacent frequency bins. This results in the extraction of compact order singular values and their corresponding singular vectors. The method is evaluated through experiments conducted on an ensemble of randomised polynomial matrices, demonstrating its superior performance in terms of higher decomposition accuracy and lower polynomial order compared to state-of-the-art techniques.",

keywords = "singular value decomposition, polynomial matrices, decomposition",

author = "Bakhit, {Mohammed A.} and Khattak, {Faizan A.} and Proudler, {Ian K.} and Stephan Weiss and Rice, {Garrey W.}",

note = "{\textcopyright} 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.; 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP ; Conference date: 10-12-2023 Through 13-12-2023",

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month = jan,

day = "31",

doi = "10.1109/CAMSAP58249.2023.10403445",

language = "English",

pages = "416--420",

booktitle = "2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)",

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Bakhit, MA , Khattak, FA , Proudler, IK , Weiss, S & Rice, GW 2024, Compact order polynomial singular value decomposition of a matrix of analytic functions. in 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). IEEE, Piscataway, NJ, pp. 416-420, 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Los Suenos, Costa Rica, 10/12/23. https://doi.org/10.1109/CAMSAP58249.2023.10403445

Compact order polynomial singular value decomposition of a matrix of analytic functions. / Bakhit, Mohammed A.; Khattak, Faizan A.; Proudler, Ian K. et al.
2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). Piscataway, NJ: IEEE, 2024. p. 416-420.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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AU - Bakhit, Mohammed A.

AU - Khattak, Faizan A.

AU - Proudler, Ian K.

AU - Weiss, Stephan

AU - Rice, Garrey W.

N1 - © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2024/1/31

Y1 - 2024/1/31

N2 - This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD for analytic, non-multiplexed polynomial matrices. The proposed method calculates a conventional SVD in sample points on the unit circle, and then applies phase smoothing algorithms to establish phase-coherence between adjacent frequency bins. This results in the extraction of compact order singular values and their corresponding singular vectors. The method is evaluated through experiments conducted on an ensemble of randomised polynomial matrices, demonstrating its superior performance in terms of higher decomposition accuracy and lower polynomial order compared to state-of-the-art techniques.

AB - This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD for analytic, non-multiplexed polynomial matrices. The proposed method calculates a conventional SVD in sample points on the unit circle, and then applies phase smoothing algorithms to establish phase-coherence between adjacent frequency bins. This results in the extraction of compact order singular values and their corresponding singular vectors. The method is evaluated through experiments conducted on an ensemble of randomised polynomial matrices, demonstrating its superior performance in terms of higher decomposition accuracy and lower polynomial order compared to state-of-the-art techniques.

KW - singular value decomposition

KW - polynomial matrices

KW - decomposition

U2 - 10.1109/CAMSAP58249.2023.10403445

DO - 10.1109/CAMSAP58249.2023.10403445

M3 - Conference contribution book

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EP - 420

BT - 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

PB - IEEE

CY - Piscataway, NJ

T2 - 9th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

Y2 - 10 December 2023 through 13 December 2023

ER -

Compact order polynomial singular value decomposition of a matrix of analytic functions

Abstract

Workshop

Keywords

Access to Document

Fingerprint

Projects

Signal Processing in the Information Age (UDRC III)

Research output

On properties and structure of the analytic singular value decomposition

Cite this