Probabilistic Reconstruction

Probabilistic reconstruction focuses on developing methods to estimate the most likely underlying data from incomplete or noisy measurements, addressing the inherent uncertainty in many inverse problems. Current research emphasizes the use of generative models, such as diffusion models and variational autoencoders, often coupled with techniques like Thompson sampling or the alternating direction method of multipliers, to improve reconstruction accuracy and quantify uncertainty. These advancements are impacting diverse fields, from medical imaging (MRI reconstruction) and materials science (3D anomaly detection) to astrophysics (dark matter mapping) and historical linguistics (phonological reconstruction), enabling more robust and reliable inferences from complex data. The ability to quantify uncertainty is particularly crucial for applications where decisions are made directly based on the reconstructed data.