Solving inverse problems with sparse noisy data, operator splitting and physics-constrained machine learning

Inverse problems are fundamental in tasks like computer vision, where model parameters need to be estimated from observable data. We propose a novel approach that combines physics-constrained deep learning with automatic differentiation (AD) to tackle inverse problems in such as computer vision. Our method integrates variational approaches with deep learning-based algorithms by leveraging deep neural networks and AD. To handle nonconvex variational models, we employ the operator splitting technique, decomposing them into simpler sub-problems solvable using deep neural networks and AD. By combining physics-informed constraints, deep learning capabilities and operator splitting, our approach offers a promising framework for addressing inverse problems in computer vision. It bridges the gap between traditional variational methods and deep learning, providing effective solutions in the presence of noise. The integration of physics-based priors and deep learning enhances accuracy and robustness in estimating solutions, advancing the field of computer vision.