Hybrid Algebraic Iterative Reconstruction and Physics-Informed Neural Networks for Solving Inverse Problems

Abstract

Algebraic Iterative Reconstruction (AIR) methods, including ART, SIRT, and SART, are effective techniques for addressing inverse problems in tomography, medical imaging, and industrial inspection. But their ability to reconstruct things gets worse in systems that are poorly conditioned, measurements that are noisy, and projection data that is sparse. Physics-Informed Neural Networks (PINNs), on the other hand, include governing differential equations in the learning framework. This makes it possible to reconstruct solutions even when the data is limited or only partially corrupted. This article suggests a combination of AIR and PINN that combines neural training based on PDEs with iterative algebraic solvers. The AIR step makes sure that the algebraic updates are stable, and the PINN makes sure that they are consistent with the physics that underlies them. Compared to AIR or PINN methods used on their own, the numerical results show better convergence, less noise sensitivity, and higher reconstruction accuracy.