Detection, reconstruction, and characterization algorithms from noisy datain multistatic wave imaging

Habib Ammari; Josselin Garnier; Vincent Jugnon

doi:10.3934/dcdss.2015.8.389

Article Contents

2015, Volume 8, Issue 3: 389-417. Doi: 10.3934/dcdss.2015.8.389

This issue Previous Article Preface Next Article Radar cross section reduction of a cavity in the ground plane: TE polarization

Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging

1.
Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d'Ulm, 75005 Paris
2.
Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13
3.
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307

Received: May 31, 2013

Revised: December 31, 2013

Published: June 2015

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Abstract

The detection, localization, and characterization of a collection of targets embedded in a medium is an important problem in multistatic wave imaging. The responses between each pair of source and receiver are collected and assembled in the form of a response matrix, known as the multi-static response matrix. When the data are corrupted by measurement or instrument noise, the structure of the response matrix is studied by using random matrix theory. It is shown how the targets can be efficiently detected, localized and characterized. Both the case of a collection of point reflectors in which the singular vectors have all the same form and the case of small-volume electromagnetic inclusions in which the singular vectors may have different forms depending on their magnetic or dielectric type are addressed.

Keywords:

Multistatic wave imaging,
noisy data,
detection and reconstruction algorithms,
random matrices,
measurement noise,
Helmholtz equation.

Mathematics Subject Classification: Primary: 78M35, 78A46; Secondary: 15B52.

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