Normalizing Flows for Bayesian Experimental Design in Imaging Applications

Neural density estimators such as normalizing flows have shown promise for estimation of the Bayesian posterior in a variety of imaging problems. Few works have explored how to practically exploit the probabilistic information contained in the full Bayesian solution of the inverse problem. Here we explore a simple modification to conditional normalizing flow training that enables Bayesian experimental design without modifying existing architectures. Based on a relationship between the expected information gain and maximum-likelihood training of normalizing flows, we show that experimental design can be achieved with the same training objective. We first verify that our method maximizes the expected information gain using a stylized problem. Then, we demonstrate our method can solve imaging problems in large scale medical and seismic applications.

https://slim.gatech.edu/Publications/Public/Conferences/SIAMUQ/2024/oroz...