Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first...

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Autor principal:	Isaac Harris
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	direct sampling method sound soft scatterer factorization method Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/7dbe89d1909b4c7f8d5579020b7f427f
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id	oai:doaj.org-article:7dbe89d1909b4c7f8d5579020b7f427f
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spelling	oai:doaj.org-article:7dbe89d1909b4c7f8d5579020b7f427f2021-11-25T17:17:16ZDirect Sampling for Recovering Sound Soft Scatterers from Point Source Measurements10.3390/computation91101202079-3197https://doaj.org/article/7dbe89d1909b4c7f8d5579020b7f427f2021-11-01T00:00:00Zhttps://www.mdpi.com/2079-3197/9/11/120https://doaj.org/toc/2079-3197In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.Isaac HarrisMDPI AGarticledirect sampling methodsound soft scattererfactorization methodElectronic computers. Computer scienceQA75.5-76.95ENComputation, Vol 9, Iss 120, p 120 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	direct sampling method sound soft scatterer factorization method Electronic computers. Computer science QA75.5-76.95
spellingShingle	direct sampling method sound soft scatterer factorization method Electronic computers. Computer science QA75.5-76.95 Isaac Harris Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
description	In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.
format	article
author	Isaac Harris
author_facet	Isaac Harris
author_sort	Isaac Harris
title	Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
title_short	Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
title_full	Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
title_fullStr	Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
title_full_unstemmed	Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
title_sort	direct sampling for recovering sound soft scatterers from point source measurements
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/7dbe89d1909b4c7f8d5579020b7f427f
work_keys_str_mv	AT isaacharris directsamplingforrecoveringsoundsoftscatterersfrompointsourcemeasurements
_version_	1718412540072951808

Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements

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