Bayesian Inference with Plug-and-Play Priors - Imaging and Inverse Problems Seminar

Explore cutting-edge Plug & Play (PnP) methods in Bayesian imaging through this 53-minute seminar presented by Marcelo Pereyra from Heriot-Watt University. Delve into the theory, methods, and provably convergent algorithms for performing Bayesian inference with PnP priors. Learn about two innovative algorithms: PnP Unadjusted Langevin Algorithm for Monte Carlo sampling and MMSE inference, and PnP Play Stochastic Gradient Descent for MAP inference. Discover how these algorithms target a decision-theoretically optimal Bayesian model and their applications in canonical problems. Gain insights into convergence guarantees, denoising operators, and deep neural networks in imaging inverse problems. Engage with topics such as variational approaches, infinite dimensions, basin frameworks, oracle models, and gradient algorithms through practical illustrations and examples.

Introduction
Presentation
Variational Approach
Infinite Dimensions
Unknown Models
Basin Framework
Estimators
Basin computation
Training data
Denoisers
Oracle Models
Spacing Assumption
Oracle Denoiser
Gradient of Prior
Gradient Algorithms
Denoiser
Algorithms
Gradient Descent
Numerical Illustrations
Histogram
Perspective
Conclusion
Questions
Noise
Signal Dependent Noise
Yoshida Regularization
Quantum Enhanced Imaging
Priors
Computing Times