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Bayesian inference with deep generative prior has received considerableinterest for solving imaging inverse problems in many scientific andengineering fields. The selection of the prior distribution is learned from,and therefore an important representation learning of, available priormeasurements. The SA-Roundtrip, a novel deep generative prior, is introduced toenable controlled sampling generation and identify the data's intrinsicdimension. This prior incorporates a self-attention structure within abidirectional generative adversarial network. Subsequently, Bayesian inferenceis applied to the posterior distribution in the low-dimensional latent spaceusing the Hamiltonian Monte Carlo with preconditioned Crank-Nicolson (HMC-pCN)algorithm, which is proven to be ergodic under specific conditions. Experimentsconducted on computed tomography (CT) reconstruction with the MNIST andTomoPhantom datasets reveal that the proposed method outperformsstate-of-the-art comparisons, consistently yielding a robust and superior pointestimator along with precise uncertainty quantification.

Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN sampler