Algebraic determination of back-projection operators for optoacoustic tomography

The simplicity and computational efficiency of back-projection formulae have made them a popular choice in optoacoustic tomography. Nonetheless, exact back-projection formulae exist for only a small set of tomographic problems. This limitation is overcome by algebraic algorithms, but at the cost of higher numerical complexity. In this paper, we present a generic algebraic framework for calculating back-projection operators in optoacoustic tomography. We demonstrate our approach in a two-dimensional optoacoustic-tomography example and show that once the algebraic back-projection operator has been found, it achieves a comparable run time to that of the conventional back-projection algorithm, but with the superior image quality of algebraic methods.