Resolution and stability analysis in acousto-electric imaging

Habib Ammari Departement de Math ´ ematiques et Applications, Ecole Normale Sup ´ erieure, 45 Rue d’Ulm, ´ 75005 Paris, France Josselin Garnier Laboratoire de Probabilites et Mod ´ eles Al ` eatoires & Laboratoire Jacques-Louis Lions, ´ Universite Paris VII, 2 Place Jussieu, 75251 Paris Cedex 5, France Wenjia Jing Departement de Math ´ ematiques et Applications, Ecole Normale Sup ´ erieure, 45 Rue d’Ulm, ´ 75005 Paris, France

Analysis of PDEs mathscidoc:2206.03004

Inverse Problems, 28, (8), 084005, 2012.7
We consider the optimization approach to the acousto-electric imaging problem. Assuming that the electric conductivity distribution is a small perturbation of a constant, we investigate the least-squares estimate analytically using (multiple) Fourier series, and confirm the widely observed fact that acousto-electric imaging has high resolution and is statistically stable. We also analyze the case of partial data and the case of limited-view data, in which some singularities of the conductivity can still be imaged.
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@inproceedings{habib2012resolution,
  title={Resolution and stability analysis in acousto-electric imaging},
  author={Habib Ammari, Josselin Garnier, and Wenjia Jing},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622154640796975448},
  booktitle={Inverse Problems},
  volume={28},
  number={8},
  pages={084005},
  year={2012},
}
Habib Ammari, Josselin Garnier, and Wenjia Jing. Resolution and stability analysis in acousto-electric imaging. 2012. Vol. 28. In Inverse Problems. pp.084005. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622154640796975448.
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