Mathematical Challenges Arising in Thermoacoustic Tomography with Line Detectors

Thermoacoustic computed tomography (thermoacoustic CT) has thepotential to become a mayor non-invasive medical imaging method. Inthis paper we derive a general mathematical framework of a novel mea-suring setup introduced in [5]. It takes measuring data of line detectorsand offers better imaging resolution than conventional approaches basedon point-data approximation. We show that the three dimensional ther-moacoustic imaging problem reduces to the mathematical problem of re-constructing the initial data of the two dimensional wave equation fromboundary measurements of its solution. We derive and analyze an analyticreconstruction formula which allows for fast numerical implementation.