Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN
  sampler
Jiayu Qian Yuanyuan Liu Jingya Yang Qingping Zhou
Bayesian inference with deep generative prior has received considerable
interest for solving imaging inverse problems in many scientific and
engineering fields. The selection of the prior distribution is learned from,
and therefore an important representation learning of, available prior
measurements. The SA-Roundtrip, a novel deep generative prior, is introduced to
enable controlled sampling generation and identify the data's intrinsic
dimension. This prior incorporates a self-attention structure within a
bidirectional generative adversarial network. Subsequently, Bayesian inference
is applied to the posterior distribution in the low-dimensional latent space
using the Hamiltonian Monte Carlo with preconditioned Crank-Nicolson (HMC-pCN)
algorithm, which is proven to be ergodic under specific conditions. Experiments
conducted on computed tomography (CT) reconstruction with the MNIST and
TomoPhantom datasets reveal that the proposed method outperforms
state-of-the-art comparisons, consistently yielding a robust and superior point
estimator along with precise uncertainty quantification.