Initial condition recovery in nonlinear damped viscous photoacoustic tomography using a convolutional neural network-guided gradient-free optimization framework

The paper tackles the inverse problem of recovering the initial pressure distribution in photoacoustic tomography (PAT) when nonlinear acoustic propagation and viscous attenuation are present. It models these effects with a nonlinear damped viscoelastic wave equation and proves well‑posedness of the forward problem. For the inverse problem, the authors establish existence, uniqueness, and local uniqueness results, and then propose a hybrid reconstruction framework that uses a convolutional neural network to generate an initial guess followed by a gradient‑free sequential quadratic Hamiltonian optimization to enforce the PDE dynamics. Numerical experiments show that this hybrid approach yields better reconstruction quality, contrast, and robustness than either time‑reversal or CNN‑only methods.