Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography

There is an increasing interest in utilizing machine learning methods in image processing and inverse problems. A significant part of the current work in inverse problems has, however, concentrated on image reconstruction problems, and the number of studies regarding estimating the posterior distribution in the context of Bayesian inverse problems has been limited. In this chapter, we study a machine learning-based approach for estimating the posterior distribution utilizing variational autoencoders, and a recently proposed uncertainty quantification variational autoencoder. The methodology is studied with numerical simulations with applications in photoacoustic tomography, where one aims at estimating a conditional probability distribution of an initial pressure when photoacoustic pressure waves on the boundary of the target are given. The simulations show that the uncertainty quantification variational autoencoder can provide a computationally efficient method for estimating the unknown initial pressure and evaluating its reliability in photoacoustic tomography.