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arXiv · 1111.5051

Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions

Guillaume Bal·Gunther Uhlmann
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Abstract

This paper concerns the reconstruction of possibly complex-valued coefficients in a second-order scalar elliptic equation posed on a bounded domain from knowledge of several solutions of that equation. We show that for a sufficiently large number of solutions and for an open set of corresponding boundary conditions, all coefficients can be uniquely and stably reconstructed up to a well characterized gauge transformation. We also show that in some specific situations, a minimum number of such available solutions equal to $I_n=\frac12n(n+3)$ is sufficient to uniquely and globally reconstruct the unknown coefficients. This theory finds applications in several coupled-physics medical imaging modalities including photo-acoustic tomography, transient elastography, and magnetic resonance elastography.

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Guillaume Bal, Gunther Uhlmann. 2011-11-21. Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions. https://arxiv.org/abs/1111.5051

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