Target Identification Using Dictionary Matching of Generalized Polarization Tensors

Habib Ammari Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005, Paris, France Thomas Boulier Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005, Paris, France Josselin Garnier Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, 75205, Paris Cedex 13, France Wenjia Jing Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005, Paris, France Hyeonbae Kang Department of Mathematics, Inha University, Incheon, 402-751, Korea Han Wang Department of Mathematics and Applications, Ecole Normale Supérieure, 45 Rue d’Ulm, 75005, Paris, France

Analysis of PDEs Mathematical Physics Numerical Analysis and Scientific Computing Optimization and Control mathscidoc:2206.03006

Foundations of Computational Mathematics, 14, 27-62, 2013.9
The aim of this paper is to provide a fast and efficient procedure for (real-time) target identification in imaging based on matching on a dictionary of precomputed generalized polarization tensors (GPTs). The approach is based on some important properties of the GPTs and new invariants. A new shape representation is given and numerically tested in the presence of measurement noise. The stability and resolution of the proposed identification algorithm is numerically quantified. We compare the proposed GPT-based shape representation with a moment-based one.
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@inproceedings{habib2013target,
  title={Target Identification Using Dictionary Matching of Generalized Polarization Tensors},
  author={Habib Ammari, Thomas Boulier, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, and Han Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622155630149279453},
  booktitle={Foundations of Computational Mathematics},
  volume={14},
  pages={27-62},
  year={2013},
}
Habib Ammari, Thomas Boulier, Josselin Garnier, Wenjia Jing, Hyeonbae Kang, and Han Wang. Target Identification Using Dictionary Matching of Generalized Polarization Tensors. 2013. Vol. 14. In Foundations of Computational Mathematics. pp.27-62. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622155630149279453.
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