Joint reconstruction of initial pressure and sound speed distributions in 3D photoacoustic computed tomography using object-constraints

In photoacoustic computed tomography (PACT), accurate estimation of the initial pressure (IP) distribution in acoustically heterogeneous media requires knowledge of the spatially varying speed-of-sound (SOS). Although heterogeneous SOS maps can be obtained using adjunct ultrasound tomography, such integration increases system complexity, cost, and acquisition time. Joint reconstruction (JR) seeks to estimate the IP and SOS distributions directly from PACT data alone; however, the resulting inverse problem is ill-posed and non-convex, requiring effective regularization. This study evaluated a three-dimensional (3D) JR approach that stabilizes joint estimation by incorporating canonical object constraints, including support, bound, and total-variation (TV) constraints. 3D virtual imaging studies were conducted using numerical breast phantoms with heterogeneous SOS and corresponding IP distributions. JR was formulated as a constrained optimization problem and solved using a three-level grid-continuation strategy over progressively finer isotropic grids, with each finer-level reconstruction initialized by interpolation of the preceding coarser-level estimate. Compared with a tuned single-SOS universal backprojection method, the proposed JR approach produced improved IP reconstructions, particularly at depth, and yielded SOS estimates that preserved the dominant heterogeneity of the true SOS distribution. These results provide a first 3D numerical demonstration of the potential of object-constrained JR to mitigate phase-aberration artifacts and improve PACT reconstruction fidelity.