Inverse Problems

Inverse problems work backward from observations to estimate the hidden image, physical state, or system parameters that produced them, often when measurements are sparse, noisy, or ambiguous. Methods range from classical regularization and optimization to physics-informed neural networks, learned operators, and generative priors such as diffusion and flow models; Bayesian methods can also represent multiple plausible solutions and their uncertainty. Applications include medical and computational imaging, seismic exploration, spectroscopy, and identifying material or dynamical properties from sensor data. A central challenge is balancing measurement consistency with useful prior information: learned priors can recover detail but may invent unsupported structure, especially when the forward model or data differs from training, so identifiability, stability, and calibrated uncertainty remain important.