# Posterior Estimation Using Deep Learning: A Simulation Study of Compartmental Modeling in Dynamic PET

arXiv: https://arxiv.org/abs/2303.10057 · HTML: https://mlsanity.com/paper/2303.10057/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 17 Mar 2023.

## Builds on (most cited first, 4 of 4)

- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Deep Unsupervised Domain Adaptation: A Review of Recent Advances and Perspectives](https://mlsanity.com/paper/2208.07422/) (2022)
- [Invertible Neural Networks versus MCMC for Posterior Reconstruction in Grazing Incidence X-Ray Fluorescence](https://mlsanity.com/paper/2102.03189/) (2021)

## Abstract (arXiv)

Background: In medical imaging, images are usually treated as deterministic, while their uncertainties are largely underexplored. Purpose: This work aims at using deep learning to efficiently estimate posterior distributions of imaging parameters, which in turn can be used to derive the most probable parameters as well as their uncertainties. Methods: Our deep learning-based approaches are based on a variational Bayesian inference framework, which is implemented using two different deep neural networks based on conditional variational auto-encoder (CVAE), CVAE-dual-encoder and CVAE-dual-decoder. The conventional CVAE framework, i.e., CVAE-vanilla, can be regarded as a simplified case of these two neural networks. We applied these approaches to a simulation study of dynamic brain PET imaging using a reference region-based kinetic model. Results: In the simulation study, we estimated posterior distributions of PET kinetic parameters given a measurement of time-activity curve. Our proposed CVAE-dual-encoder and CVAE-dual-decoder yield results that are in good agreement with the asymptotically unbiased posterior distributions sampled by Markov Chain Monte Carlo (MCMC). The CVAE-vanilla can also be used for estimating posterior distributions, although it has an inferior performance to both CVAE-dual-encoder and CVAE-dual-decoder. Conclusions: We have evaluated the performance of our deep learning approaches for estimating posterior distributions in dynamic brain PET. Our deep learning approaches yield posterior distributions, which are in good agreement with unbiased distributions estimated by MCMC. All these neural networks have different characteristics and can be chosen by the user for specific applications. The proposed methods are general and can be adapted to other problems.