A PINN-driven game-theoretic framework in limited data photoacoustic tomography

This paper presents a novel methodological framework to obtain superior reconstructions in limited data photoacoustic tomography. The proposed framework exploits the presence of Cauchy data on an accessible part of the observation domain and uses a Nash game-theoretic framework to complete the missing data on the inaccessible region. To solve the game-theoretic problem, a gradient-free sequential quadratic Hamiltonian scheme, which is based on Pontryagin's maximum principle characterization, is combined with physics-informed neural networks to obtain the initial guess, leading to a robust and accurate reconstruction scheme. Numerical simulations with various phantoms, choice of accessible observation domains, and noise, demonstrate the effectiveness of our proposed framework to obtain high contrast and resolution reconstructions.