Variational Bayes uncertainty quantification for inverse problems

Many popular regularised estimators in linear inverse problems arising from PET and other tomographic medical imaging techniques can be interpreted as maximum a posteriori (MAP) estimators. An analysis of the full Bayesian posterior in these problems has been proposed as a procedure for uncertainty quantification, for which there is a significant need in medical applications. However, algorithms for posterior sampling can be expensive and difficult to tune. The purpose of the project is to develop variational Bayes posterior approximations of the posterior, and prove guarantees on the convergence of algorithms and on the quality of the approximation.