Abstract
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 focus 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.
Highlights
Coupled-physics inverse problems arise in various hybrid medical imaging and seismic imaging modalities
This low resolution phenomena manifests the ill-posedness of the inverse problem of reconstructing diffusive coefficients from boundary measurements
Our emphasis is on applications of complex geometrical optics (CGO) solutions in solving inverse problems with internal data arising in various imaging modalities introduced above
Summary
Coupled-physics inverse problems arise in various hybrid medical imaging and seismic imaging modalities. We observe that coupled-physics imaging methods involve solving multiple steps of inverse problems, each of which has to be well-posed (stable) to give an overall high resolution in imaging. It is a major feature of these methods that usually the last step is to solve an inverse problem with internal data obtained from previous steps. Breakthrough has been made on constructing CGO solutions to equations with less regular parameters, using an averaging technique, see [32, 46, 47] In this survey, our emphasis is on applications of CGO solutions in solving inverse problems with internal data arising in various imaging modalities introduced above.
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