Exact and approximative imaging methods for photoacoustic tomography using an arbitrary detection surface

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Abstract
Two universal reconstruction methods for photoacoustic (also called optoacoustic or thermoacoustic) computed tomography are derived, applicable to an arbitrarily shaped detection surface. In photoacoustic tomography acoustic pressure waves are induced by illuminating a semitransparent sample with pulsed electromagnetic radiation and are measured on a detection surface outside the sample. The imaging problem consists in reconstructing the initial pressure sources from those measurements. The first solution to this problem is based on the time reversal of the acoustic pressure field with a second order embedded boundary method. The pressure on the arbitrarily shaped detection surface is set to coincide with the measured data in reversed temporal order. In the second approach the reconstruction problem is solved by calculating the far-field approximation, a concept well known in physics, where the generated acoustic wave is approximated by an outgoing spherical wave with the reconstruction point as center. Numerical simulations are used to compare the proposed universal reconstruction methods with existing algorithms.