This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT), Thermo-acoustic Tomography (TAT), Electro-Seismic Conversion, Transient Elastrography (TE) and Acousto-Electric Tomography (AET). These inverse problems typically consists of multiple inverse steps, each of which corresponds to one of the wave propagations involved. The review focuses on those steps known as the inverse problems with internal data, in which the complex geometrical optics (CGO) solutions to the underlying equations turn out to be useful in showing the uniqueness and stability in determining the desired information.
Bibliographical noteFunding Information:
R.-Y. L. was partly supported by the AMS-Simons Travel Grants. TZ. was supported by NSF grant DMS-1501049 and Alfred P. Sloan Research Fellowship FR-2015-65641.
©2017 American Institute of Mathematical Sciences.
- CGO solutions
- Coupled-physics imaging modalities
- Internal data