Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array
The resolution related with the image quality of acoustic imaging using a microphone array is limited by the size and density of the array. However, non-synchronous measurements can exceed the constraints defined by measurements with a single fixed array. The non-synchronous measurements can achieve...
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doaj-648c853b89764681bd575080313a11442021-03-30T15:14:37ZengIEEEIEEE Access2169-35362021-01-019219512196410.1109/ACCESS.2021.30557289343256Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones ArrayLiang Yu0https://orcid.org/0000-0001-8079-4055Yi Fan1Ning Chu2https://orcid.org/0000-0003-1514-873XQian Huang3https://orcid.org/0000-0002-6248-080XYue Ning4https://orcid.org/0000-0002-5981-2121Peng Hou5State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, ChinaHagong Intelligent Robot Company Ltd., Shanghai, ChinaCollege of Energy Engineering, Institute of Process Equipment, Zhejiang University, Hangzhou, ChinaCollege of Energy Engineering, Institute of Process Equipment, Zhejiang University, Hangzhou, ChinaCollege of Energy Engineering, Institute of Process Equipment, Zhejiang University, Hangzhou, ChinaInstitute of Science and Technology on Underwater test and Control, Dalian, ChinaThe resolution related with the image quality of acoustic imaging using a microphone array is limited by the size and density of the array. However, non-synchronous measurements can exceed the constraints defined by measurements with a single fixed array. The non-synchronous measurements can achieve a larger and denser aperture array by moving the single array. The key problem of archiving the non-synchronous measurements of a microphone array is the matrix completion of a block diagonal spectral matrix. A comprehensive investigation of the block diagonal spectral matrix completion is still missing in the microphone array signal processing literature since it is usually considered as a difficult problem if without the integrated physical information of the sound field. In this paper, the mathematical relation between the max-norm and the nuclear-norm is pointed out, and the max-norm minimization of the spectral matrix is discussed, which is an effective model with integrated spatial representation of the sound field for the spectral matrix completion. First, the max-norm is utilized for the low complexity modeling and the corresponding Proximal-Point method for Max-norm based Spectral matrix completion (PPMSMC) is proposed; Second, the rank, nuclear-norm and max-norm have been investigated as complexity measures in the context of spectral matrix completion, and their performances are compared. The proposed low-rank methods have constructed a concrete theorem foundation for the non-synchronous measurements of the microphone array.https://ieeexplore.ieee.org/document/9343256/Acoustic measurementslow complexity modelmax-norm minimization |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Liang Yu Yi Fan Ning Chu Qian Huang Yue Ning Peng Hou |
spellingShingle |
Liang Yu Yi Fan Ning Chu Qian Huang Yue Ning Peng Hou Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array IEEE Access Acoustic measurements low complexity model max-norm minimization |
author_facet |
Liang Yu Yi Fan Ning Chu Qian Huang Yue Ning Peng Hou |
author_sort |
Liang Yu |
title |
Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array |
title_short |
Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array |
title_full |
Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array |
title_fullStr |
Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array |
title_full_unstemmed |
Low Complexity Modeling of Cross-Spectral Matrix and Its Application in the Non-Synchronous Measurements of Microphones Array |
title_sort |
low complexity modeling of cross-spectral matrix and its application in the non-synchronous measurements of microphones array |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2021-01-01 |
description |
The resolution related with the image quality of acoustic imaging using a microphone array is limited by the size and density of the array. However, non-synchronous measurements can exceed the constraints defined by measurements with a single fixed array. The non-synchronous measurements can achieve a larger and denser aperture array by moving the single array. The key problem of archiving the non-synchronous measurements of a microphone array is the matrix completion of a block diagonal spectral matrix. A comprehensive investigation of the block diagonal spectral matrix completion is still missing in the microphone array signal processing literature since it is usually considered as a difficult problem if without the integrated physical information of the sound field. In this paper, the mathematical relation between the max-norm and the nuclear-norm is pointed out, and the max-norm minimization of the spectral matrix is discussed, which is an effective model with integrated spatial representation of the sound field for the spectral matrix completion. First, the max-norm is utilized for the low complexity modeling and the corresponding Proximal-Point method for Max-norm based Spectral matrix completion (PPMSMC) is proposed; Second, the rank, nuclear-norm and max-norm have been investigated as complexity measures in the context of spectral matrix completion, and their performances are compared. The proposed low-rank methods have constructed a concrete theorem foundation for the non-synchronous measurements of the microphone array. |
topic |
Acoustic measurements low complexity model max-norm minimization |
url |
https://ieeexplore.ieee.org/document/9343256/ |
work_keys_str_mv |
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