Applications of CGO Solutions on Coupled-Physics Inverse Problems

TL;DR

This paper reviews how complex geometrical optics (CGO) solutions are used to address inverse problems with internal data in various coupled-physics imaging modalities, enhancing understanding of uniqueness and stability.

Contribution

It provides a comprehensive survey of the application of CGO solutions to inverse problems in multiple coupled-physics imaging techniques, highlighting their role in proving uniqueness and stability.

Findings

CGO solutions aid in establishing uniqueness in inverse problems.

CGO solutions contribute to stability analysis in coupled-physics imaging.

The review covers applications in medical and geophysical imaging modalities.

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.