Reconstructions for some coupled-physics inverse problems

TL;DR

This paper reviews and extends methods for reconstructing coefficients in elliptic equations from multiple solutions, applying to various hybrid imaging modalities with stability estimates.

Contribution

It extends previous work to identify reconstructable parameters and provides stability estimates for coupled-physics inverse problems.

Findings

Reconstruction procedures for elliptic coefficients are applicable to multiple imaging modalities.

Certain parameters are identifiable while others are not in hybrid imaging.

Stability estimates are established for the reconstruction process.

Abstract

This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct 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.