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As the most successful example of a hybrid tomographic technique,photoacoustic tomography is based on generating acoustic waves inside an objectof interest by stimulating electromagnetic waves. This acoustic wave ismeasured outside the object and converted into a diagnostic image. Onemathematical problem is determining the initial function from the measureddata. The initial function describes the spatial distribution of energyabsorption, and the acoustic wave satisfies the wave equation with variablespeed. In this article, we consider two types of problems: inverse problem withRobin boundary condition and inverse problem with Dirichlet boundary condition.We define two wave-forward operators that assign the solution of the waveequation based on the initial function to a given function and provide theirinversions.

Inversions of two wave-forward operators with variable coefficients