Reconstructions for some coupled-physics inverse problems

This letter announces and summarizes results obtained in Bal and Uhlmann (2011) [1] and considers several natural extensions. The aforementioned paper proposes a procedure for reconstructing coefficients in a second-order, scalar, elliptic equation from knowledge of a sufficiently large number of its solutions. We present this derivation and extend it to show which parameters may or may not be reconstructed for several hybrid (also called coupled-physics) imaging modalities including photo-acoustic tomography, thermo-acoustic tomography, transient elastography, and magnetic resonance elastography. Stability estimates are also proposed.