Parameterized joint reconstruction of the initial pressure and sound speed distributions in photoacoustic computed tomography
Accurate estimation of the initial pressure distribution in photoacoustic computed tomography (PACT) requires some knowledge of the sound speed distribution. However, the sound speed distribution is typically unknown. Further, the initial pressure and sound speed distributions cannot both, in general, be stably recovered from PACT measurements alone. In this work, a joint reconstruction method for the initial pressure distribution and a low-dimensional parameterized model of the sound speed distribution is proposed. By employing a priori information about the structure of the sound speed distribution, both the initial pressure and sound speed can be accurately recovered. The joint reconstruction problem is solved by use of a proximal optimization method that allows constraints and non-smooth regularization functions for initial pressure distribution. The gradients of the cost function with respect to the initial pressure and sound speed distributions are calculated by use of an adjoint state method that has the same per-iteration computational cost as calculating the gradient with respect to the initial pressure distribution alone. This approach is quantitatively evaluated through 2D computer-simulation studies for a small animal imaging model. The impact of the choice of the parameterized sound speed model is investigated. Even when the assumed parameterized sound speed model is inconsistent with the true sound speed distribution, the estimated initial pressure distribution is more accurate than that obtained by assuming a constant sound speed. The utility of the proposed approach is also demonstrated through application to experimental in vivo measurements of a mouse.