The inverse source problem arising in Photoacoustic Tomography

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The project addresses fundamental analytical questions on the acoustic waveequation. The questions arise in, but are not limited to the context ofPhotoacoustic Tomography (PAT). PAT is a medical imaging technique that combines the high contrast inelectromagnetic absorption, say between healthy and cancerous tissue, with thehigh resolution of ultrasound. The existing PAT image reconstruction methodsbased on time-reversal arguments do not work when photoacoustic measurementsare obtained by using an array of detectors that reflects acoustic waves.However, the use of detector arrays significantly speeds up the dataacquisition in practice. One of the main objectives of the project is todevelop a comprehensive analytical theory for PAT in a reflecting cavityformed by detector arrays. The mathematical results to be obtained have applications beyond PAT in thefields of Control Theory for Partial Differential Equations and InverseProblems. These applications will be explored. In particular, the resultsallow us to understand better the stability properties of hyperbolic inverseboundary value problems. These problems occur in a large number ofapplications including medical ultrasound tomography, seismology, oceanology,process monitoring and non-destructive testing. In terms of theseapplications, our focus is on seismic imaging.