Ill Posed Inverse Problem

Ill-posed inverse problems, where solutions are either non-unique or highly sensitive to noise, are a central challenge across numerous scientific fields. Current research focuses on developing robust regularization techniques, often integrating deep learning architectures like neural networks (including implicit neural representations and unrolled optimization algorithms) and generative models (such as diffusion models and normalizing flows) to incorporate prior information and improve solution stability. These advancements are significantly impacting diverse applications, from medical imaging (e.g., CT, MRI) and geophysical imaging to robotics and material science, enabling more accurate and reliable reconstructions from incomplete or noisy data. The development of efficient algorithms, including those based on stochastic optimization and Krylov subspace methods, is also a key area of focus to address the computational demands of large-scale problems.