Bayesian inverse problems with neural generative priors
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2022
Författare
Molin, Vincent
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Inverse problems are ubiquitous in medical imaging and their solutions are essential
for clinical decision making. To allow for quantification of uncertainty a Bayesian
approach can be taken, but selecting an informed prior is highly non-trivial. We
present a data-driven framework where a generative neural network in the form of a
Wasserstein Generative Adversarial Network (WGAN) learns a realistic prior, decoupled
from the inverse problem in consideration. The method is tested on a severely
undersampled two dimensional MRI analogue. We use two different Markov chain
Monte Carlo algorithms for approximating the resulting posterior expectations, one
based on piecewise deterministic Markov processes, as well as the preconditioned
Crank-Nicolson algorithm. The posterior mean and standard deviation is computed
for the reconstructions. Our experiments demonstrate that this approach outperforms
classical imaging priors both in the quality of reconstructions and also yielding
a realistic posterior, allowing for sharp reconstructions with uncertainty using only
a sparse observation.
Beskrivning
Ämne/nyckelord
Inverse problems, Markov chain Monte Carlo, generative modelling, piecewise deterministic Markov processes