Photoacoustic inversion formulas using mixed data on finite time intervals

Abstract

We study the inverse source problem in photoacoustic tomography (PAT) for mixed data, which is a weighted linear combination of the acoustic pressure wave and its normal gradient on an observation surface. We consider the case where the data is only available on finite time intervals which accounts for real-world usage of PAT. Extending our previous work, we derive explicit formulas up to a smoothing integral on convex domains with a smooth boundary, yielding exact reconstruction for circular or elliptical domains. We also present numerical reconstruction of our new exact inversion formulas on finite time intervals and compare them with the reconstructions of our previous formulas for unlimited time wave measurements.