Bayesian inverse problems with neural generative priors

dc.contributor.authorMolin, Vincent
dc.contributor.departmentChalmers tekniska högskola / Institutionen för matematiska vetenskapersv
dc.contributor.examinerBeilina, Larisa
dc.contributor.supervisorRingh, Axel
dc.contributor.supervisorSchauer, Moritz
dc.date.accessioned2022-06-19T17:17:04Z
dc.date.available2022-06-19T17:17:04Z
dc.date.issued2022sv
dc.date.submitted2020
dc.description.abstractInverse 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.sv
dc.identifier.coursecodeMVEX03sv
dc.identifier.urihttps://hdl.handle.net/20.500.12380/304782
dc.language.isoengsv
dc.setspec.uppsokPhysicsChemistryMaths
dc.subjectInverse problems, Markov chain Monte Carlo, generative modelling, piecewise deterministic Markov processessv
dc.titleBayesian inverse problems with neural generative priorssv
dc.type.degreeExamensarbete för masterexamensv
dc.type.uppsokH
local.programmeEngineering mathematics and computational science (MPENM), MSc
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