Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems

arXiv:2511.12257 · stat.CO, cs.CV, eess.IV, stat.ML · Submitted 2025-11-15 · Read on arXiv

stat.CO, cs.CV, eess.IV, stat.ML

Submitted: 2025-11-15

Updated: 2026-09-25

Terminology

• Regularization — 44× in this paper · explained in 3 episodes
• Inverse Problem — 26× in this paper · explained in 2 episodes
• Data Augmentation — 11× in this paper · explained in 7 episodes
• Fidelity — 11× in this paper · explained in 2 episodes
• Bayesian Framework — 8× in this paper · explained in 3 episodes
• Hessian Riemannian Langevin Monte Carlo — 6× in this paper
• Calibration — 5× in this paper · explained in 7 episodes
• Score Function — 5× in this paper · explained in 4 episodes
• Uncertainty Quantification — 4× in this paper · explained in 8 episodes
• Bayesian Inference — 3× in this paper · explained in 5 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Interpretability — 3× in this paper · explained in 15 episodes
• Sparsity — 3× in this paper · explained in 4 episodes
• Decoupling — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Alternating Direction Method of Multipliers — 1× in this paper
• Alternating Direction Method of Multipliers (ADMM) — 1× in this paper · explained in 2 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Computer Vision Pattern Recognition — 1× in this paper
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 3 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Learned Perceptual Image Patch Similarity — 1× in this paper
• Poisson Image Deconvolution by Augmented Lagrangian — 1× in this paper
• Robustness — 1× in this paper · explained in 5 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 4 episodes

Sources

• A Hierarchical Bayesian Framework for Constructing Sparsity-inducing Priors
• Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems

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