Summary
Photoacoustic tomography is a medical imaging technique that captures images by detecting sound waves produced by light absorption in tissues. The researchers studied how to better reconstruct the original pressure distribution inside the body from these sound waves, even when the sound behaves in complex nonlinear and damped ways. They combined a special type of neural network with a gradient-free optimization method to guide the reconstruction process, making it more accurate and robust. Their approach worked better than previous methods that used only neural networks or traditional techniques on their own.
What this means in practice
- •For biomedical imaging engineers: Enhance image reconstruction accuracy in photoacoustic tomography systems to better capture initial pressure conditions with nonlinear and damping effects considered.
- •For ultrasound device developers: Incorporate hybrid AI and physics-based optimization algorithms into device software to improve image quality despite complex acoustic behaviors.
Authors
Madhu Gupta, Anwesa Dey, Prapti Tala, Souvik Roy
Abstract
Photoacoustic tomography (PAT) is a hybrid imaging modality that combines high optical contrast with high ultrasonic resolution for biomedical imaging applications. In this work, we investigate the inverse problem of recovering the initial pressure distribution from boundary measurements in the presence of nonlinear acoustic propagation and viscous attenuation effects. To model these phenomena more accurately, we consider a nonlinear damped viscoelastic wave equation incorporating spatially varying sound speed, temporal attenuation, and nonlinear propagation mechanisms. We first establish the well-posedness of the corresponding forward problem using a Galerkin approximation combined with energy estimates and a fixed-point argument. For the inverse problem, we derive existence, uniqueness, and local uniqueness results under suitable assumptions through a harmonic extension reduction, spectral Laplace transform techniques, and observability estimates. To numerically reconstruct the initial pressure field, we develop a hybrid reconstruction framework that combines a convolutional neural network (CNN) with a gradient-free optimization strategy based on the sequential quadratic Hamiltonian (SQH) method derived from Pontryagin's maximum principle. The CNN is used to generate an informative initial guess, while the SQH framework enforces the governing PDE dynamics during the reconstruction process. Numerical experiments demonstrate that the proposed hybrid strategy significantly improves reconstruction quality, contrast, and robustness compared to standalone time-reversal and CNN-based approaches.