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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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# Imaging of complex-valued tensors for two-dimensional Maxwell’s equations

Chenxi Guo
• Corresponding author
• Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, 10027, USA
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• Other articles by this author:
/ Guillaume Bal
Published Online: 2016-05-12 | DOI: https://doi.org/10.1515/jiip-2015-0013

## Abstract

This paper concerns the imaging of a complex-valued anisotropic tensor $\gamma =\sigma +𝜾\omega \epsilon$ from knowledge of several inter magnetic fields H, where H satisfies the anisotropic Maxwell system on a bounded domain $X\subset {ℝ}^{2}$ with prescribed boundary conditions on $\partial X$. We show that γ can be uniquely reconstructed with a loss of two derivatives from errors in the acquisition H. A minimum number of five well-chosen functionals guaranties a local reconstruction of γ in dimension two. The explicit inversion procedure is presented in several numerical simulations, which demonstrate the influence of the choice of boundary conditions on the stability of the reconstruction. This problem finds applications in the medical imaging modalities Current Density Imaging and Magnetic Resonance Electrical Impedance Tomography.

MSC 2010: 35J99; 35R30; 92C55

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Revised: 2015-12-28

Accepted: 2016-03-30

Published Online: 2016-05-12

Published in Print: 2017-04-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 2, Pages 195–205, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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