MATS577: MA1: Multiwave Imaging (JSS23)

by Elina Kaarina Leskinen last modified Aug 23, 2013 01:02 PM
Multi-wave 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 a high (sub-millimeter) resolution, but suffers from low contrast. On the other hand, many tumors absorb much more energy of electromagnetic waves (in some specific energy bands) than healthy cells. Photoacoustic tomography (PAT) consists of sending relatively harmless optical radiation into tissues that causes heating which results in the generation of propagating ultrasound waves (the photo-acoustic effect). Such ultrasonic waves are readily measurable. The inverse problem then consists of reconstructing the optical properties of the tissue from these measurements. In Thermoacoustic tomography (TAT) low frequency microwaves, with wavelengths on the order of $1m$, are sent into the medium. The rationale for using the latter frequencies is that they are less absorbed than optical frequencies. Transient Elastography (TE) images the propagation of shear waves using ultrasound. Multi-wave imaging methods lead to a rich supply of new mathematical questions that involve elliptic and hyperbolic partial differential equations. We will discuss some of the inverse problems arising in these imaging techniques with emphasis on PAT.