Implicit learning to determine variable sound speed and the reconstruction operator in photoacoustic tomography

Photoacoustic tomography (PAT) is a hybrid medical imaging technique that offers both high contrast and a high spatial resolution. One challenging mathematical problem associated with PAT is reconstructing the initial pressure of the wave equation from data collected at the specific surface where the detectors are positioned. This study addresses this problem when PAT is modeled by a wave equation with unknown sound speed [Formula: see text], which is a function of spatial variables, and under the assumption that both the Dirichlet and Neumann boundary values on the detector surface are measured. In practice, we propose a novel implicit learning framework that uses Cauchy data-comprising both Dirichlet and Neumann boundary data-to simultaneously estimate the unknown sound speed and the reconstruction operator. Our framework exhibits strong robustness to measurement noise, which is inevitable in real-world settings. The experimental results demonstrate that the proposed framework maintains high reconstruction fidelity and stable convergence even under significant noise levels (up to 20%).