Revisiting the joint estimation of initial pressure and speed-of-sound distributions in photoacoustic computed tomography with consideration of canonical object constraints

In photoacoustic computed tomography (PACT) the accurate estimation of the initial pressure (IP) distribution generally requires knowledge of the object's heterogeneous speed-of-sound (SOS) distribution. Although hybrid imagers that combine ultrasound tomography with PACT have been proposed, in many current applications of PACT the SOS distribution remains unknown. Joint reconstruction (JR) of the IP and SOS distributions from PACT measurement data alone can address this issue. However, this joint estimation problem is ill-posed and corresponds to a non-convex optimization problem. While certain regularization strategies have been deployed, stabilizing the JR problem to yield accurate estimates of the IP and SOS distributions has remained an open challenge. To address this, the presented numerical studies explore the effectiveness of easy to implement canonical object constraints for stabilizing the JR problem. The considered constraints include support, bound, and total variation constraints, which are incorporated into an optimization-based method for JR. Computer-simulation studies that employ anatomically realistic numerical breast phantoms are conducted to evaluate the impact of these object constraints on JR accuracy. Additionally, the impact of certain data inconsistencies, such as caused by measurement noise and physics modeling mismatches, on the effectiveness of the object constraints is investigated. The results demonstrate, for the first time, that the incorporation of canonical object constraints in an optimization-based image reconstruction method holds significant potential for mitigating the ill-posed nature of the PACT JR problem.