The Gaussian Latent Machine: Efficient Prior and Posterior Sampling for Inverse Problems
This work addresses sampling challenges in Bayesian imaging, offering a novel method that improves efficiency for inverse problems, though it appears incremental as it builds on existing sampling techniques.
The paper tackles the problem of sampling from product-of-experts models in Bayesian imaging by introducing the Gaussian latent machine, a latent variable model that unifies and generalizes existing sampling algorithms, resulting in an efficient two-block Gibbs sampling approach with demonstrated effectiveness in numerical experiments.
We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent variable model, which we refer to as a Gaussian latent machine. This leads to a general sampling approach that unifies and generalizes many existing sampling algorithms in the literature. Most notably, it yields a highly efficient and effective two-block Gibbs sampling approach in the general case, while also specializing to direct sampling algorithms in particular cases. Finally, we present detailed numerical experiments that demonstrate the efficiency and effectiveness of our proposed sampling approach across a wide range of prior and posterior sampling problems from Bayesian imaging.