The University of Southampton
University of Southampton Institutional Repository

Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods

Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods
Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods
One method for deducing the strength of an acoustic source distribution from measurement of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution. In practice, the frequency response function matrix to be inverted may very often be ill-conditioned. This ill-conditioning will also often result in an ill-posed problem and thus regularization algorithms are used to produce reasonable solutions. For this purpose, Tikhonov regularization has been applied, and generalized cross-validation (GCV) has been introduced as an effective method for determining the proper amount of regularization without prior knowledge of either the source distribution or the contaminating errors. In the present work, the emphasis is placed on the relationship between the spatial resolution of the reconstructed source distribution and the small singular values of the frequency response function matrix to be inverted. However, the use of Tikhonov regularization often suppresses the effect of small singular values and these are in turn often associated with high spatial frequencies of the source distribution. Thus, the process of regularization produces a useful estimate of the acoustic source strength distribution but with a limited spatial resolution. Furthermore, in the field of Fourier acoustics, the spatial resolution of the reconstructed source distribution is usually limited by the wavelength of the radiation. This paper expresses the relationship between estimation accuracy, spatial resolution, noise-level and source/sensor geometry, when a range of inverse sound radiation problems are regularised using Tikhonov regularization with GCV. The results presented form the basis of guidelines that enable the reconstruction of acoustic source strength with a resolution that is finer than the intrinsic half-wavelength limit.
0022-460X
583-608
Kim, Y.
1b151f34-277a-4414-b508-f944c626d90d
Nelson, P.A.
5c6f5cc9-ea52-4fe2-9edf-05d696b0c1a9
Kim, Y.
1b151f34-277a-4414-b508-f944c626d90d
Nelson, P.A.
5c6f5cc9-ea52-4fe2-9edf-05d696b0c1a9

Kim, Y. and Nelson, P.A. (2003) Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods. Journal of Sound and Vibration, 265 (3), 583-608. (doi:10.1016/S0022-460X(02)01452-9).

Record type: Article

Abstract

One method for deducing the strength of an acoustic source distribution from measurement of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution. In practice, the frequency response function matrix to be inverted may very often be ill-conditioned. This ill-conditioning will also often result in an ill-posed problem and thus regularization algorithms are used to produce reasonable solutions. For this purpose, Tikhonov regularization has been applied, and generalized cross-validation (GCV) has been introduced as an effective method for determining the proper amount of regularization without prior knowledge of either the source distribution or the contaminating errors. In the present work, the emphasis is placed on the relationship between the spatial resolution of the reconstructed source distribution and the small singular values of the frequency response function matrix to be inverted. However, the use of Tikhonov regularization often suppresses the effect of small singular values and these are in turn often associated with high spatial frequencies of the source distribution. Thus, the process of regularization produces a useful estimate of the acoustic source strength distribution but with a limited spatial resolution. Furthermore, in the field of Fourier acoustics, the spatial resolution of the reconstructed source distribution is usually limited by the wavelength of the radiation. This paper expresses the relationship between estimation accuracy, spatial resolution, noise-level and source/sensor geometry, when a range of inverse sound radiation problems are regularised using Tikhonov regularization with GCV. The results presented form the basis of guidelines that enable the reconstruction of acoustic source strength with a resolution that is finer than the intrinsic half-wavelength limit.

This record has no associated files available for download.

More information

Published date: 14 August 2003

Identifiers

Local EPrints ID: 10380
URI: http://eprints.soton.ac.uk/id/eprint/10380
ISSN: 0022-460X
PURE UUID: 92989737-f5b8-4ec8-a607-32d337adb6aa
ORCID for P.A. Nelson: ORCID iD orcid.org/0000-0002-9563-3235

Catalogue record

Date deposited: 23 May 2005
Last modified: 16 Mar 2024 02:32

Export record

Altmetrics

Contributors

Author: Y. Kim
Author: P.A. Nelson ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×