Can one see the sound of light?
Mathematics of photoacoustic tomography
Photoacoustic tomography is a rapidly developing modality for in vivo imaging. The method is used in various fields like spectroscopy, microscopy, and biomedicine. Especially biomedical applications seem to attract increasing attention. The method is based on the generation of an acoustic wave due to absorption of energy. A very short laser pulse is sent to a probe where, triggered by the absorption of the in-falling radiation, a thermoelastic expansion of the tissue is initiated. This expansion creates a pressure wave which propagates through the probe and beyond. The corresponding acoustic signal is recorded by transducers which are distributed around the object. The aim is to reconstruct an image from these signals.
The talk will provide an overview on the mathematical models used in photoacoustic tomography and some fundamental related results. Moreover, we will present several reconstruction techniques and a new exact inversion formula.