Reconstruction of coefficients in scalar second-order elliptic equations from knowledge of their solutions
نویسندگان
چکیده
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 In = 1 2n(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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