Full field inversion in photoacoustic tomography with variable sound speed
For researchers in photoacoustic imaging, this method improves reconstruction accuracy when sound speed varies, addressing a practical limitation of existing approaches.
The paper addresses photoacoustic tomography with full field detection, where existing methods assume constant sound speed, leading to errors. They propose a two-step reconstruction method that accounts for variable sound speed and demonstrate its uniqueness and stability.
Recently, a novel measurement setup has been introduced to photoacoustic tomography, that collects data in the form of projections of the full 3D acoustic pressure distribution at a certain time instant. Existing imaging algorithms for this kind of data assume a constant speed of sound. This assumption is not always met in practice and thus leads to erroneous reconstructions. In this paper, we present a two-step reconstruction method for full field detection photoacoustic tomography that takes variable speed of sound into account. In the first step, by applying the inverse Radon transform, the pressure distribution at the measurement time is reconstructed point-wise from the projection data. In the second step, one solves a final time wave inversion problem where the initial pressure distribution is recovered from the known pressure distribution at the measurement time. For the latter problem, we derive an iterative solution approach, compute the required adjoint operator, and show its uniqueness and stability.