# American Institute of Mathematical Sciences

December  2017, 11(6): 1027-1046. doi: 10.3934/ipi.2017047

## Some remarks on the small electromagnetic inhomogeneities reconstruction problem

 Sorbonne University, Université de Technologie de Compiègne, Laboratoire de Mathématiuqes Appliquées de Compiègne LMAC, 60205 Compiègne Cedex, France

* Corresponding author: Abdellatif El Badia

Received  October 2016 Revised  July 2017 Published  September 2017

This work considers the problem of recovering small electromagnetic inhomogeneities in a bounded domain $Ω \subset \mathbb{R}^3$, from a single Cauchy data, at a fixed frequency. This problem has been considered by several authors, in particular in [4]. In this paper, we revisit this work with the objective of providing another identification method and establishing stability results from a single Cauchy data and at a fixed frequency. Our approach is based on the asymptotic expansion of the boundary condition derived in [4] and the extension of the direct algebraic algorithm proposed in [1].

Citation: Batoul Abdelaziz, Abdellatif El Badia, Ahmad El Hajj. Some remarks on the small electromagnetic inhomogeneities reconstruction problem. Inverse Problems & Imaging, 2017, 11 (6) : 1027-1046. doi: 10.3934/ipi.2017047
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