Nonparametric posterior learning for emission tomography with multimodal data

TL;DR

This paper introduces a scalable nonparametric posterior learning method for uncertainty quantification in emission tomography with multimodal data, improving computational efficiency and providing theoretical guarantees.

Contribution

It adapts nonparametric posterior learning to Poisson data in emission tomography, deriving parallelizable algorithms with theoretical consistency and new geometrical conditions for multimodal data integration.

Findings

Algorithms are trivially parallelizable and scalable.

Theoretical proof of consistency and tightness in the small noise limit.

Compared to MCMC, our method reduces mixing times and computational complexity.

Abstract

We continue studies of the uncertainty quantification problem in emission tomographies such as PET or SPECT when additional multimodal data (e.g., anatomical MRI images) are available. To solve the aforementioned problem we adapt the recently proposed nonparametric posterior learning technique to the context of Poisson-type data in emission tomography. Using this approach we derive sampling algorithms which are trivially parallelizable, scalable and very easy to implement. In addition, we prove conditional consistency and tightness for the distribution of produced samples in the small noise limit (i.e., when the acquisition time tends to infinity) and derive new geometrical and necessary condition on how MRI images must be used. This condition arises naturally in the context of identifiability problem for misspecified generalized Poisson models. We also contrast our approach with Bayesian Markov Chain Monte Carlo sampling based on one data augmentation scheme which is very popular in the context of Expectation-Maximization algorithms for PET or SPECT. We show theoretically and also numerically that such data augmentation significantly increases mixing times for the Markov chain. In view of this, our algorithms seem to give a reasonable trade-off between design complexity, scalability, numerical load and assessment for the uncertainty.