Multiwave methods via ultrasound

Summary

We survey recent results by the authors on multiwave methods where the high-resolution method is ultrasound. We consider the inverse problem of determining a source inside a medium from ultrasound measurements made on the boundary of the medium. Some multiwave medical imaging methods where this is considered are photoacoustic tomography, thermoacoustic tomography, ultrasound modulated tomography, transient elastography and magnetoacoustic tomography. In the case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary. We study the case of a smooth speed and speeds having jump type of singularities. The latter models propagation of acoustic waves in the brain, where the skull has a much larger sound speed than the rest of the brain. In this paper we emphasize a microlocal viewpoint.

Multiwave imaging methods, also called hybrid methods, attempt to combine the high resolution of one imaging method with the high contrast capabilities of another through a physical principle. One important medical imaging application is breast cancer detection. Ultrasound provides high (submillimeter) resolution, but it suffers from low contrast. On the other hand, many tumors absorb much more energy from electromagnetic waves (in some specific energy bands) than healthy cells. Photoacoustic tomography (PAT) [Wang 2009] consists of exposing tissues to relatively harmless optical radiation that causes temperature increases in the millikelvin range, resulting in the generation of propagating ultrasound waves (the photoacoustic effect). Such ultrasonic waves are readily measurable. The inverse problem then consists of reconstructing the optical properties of the tissue. In thermoacoustic tomography (TAT)—see, e.g., [Kruger et al. 1999]— low frequency microwaves, with wavelengths on the order of 1 m, are sent into the medium.