Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN sampler
This work addresses CT reconstruction for scientific and engineering fields, offering an incremental improvement with a novel prior and sampling method.
The paper tackled the imaging inverse problem in computed tomography (CT) reconstruction by introducing the SA-Roundtrip deep generative prior and using HMC-pCN for Bayesian inference, resulting in outperforming state-of-the-art methods with robust point estimators and precise uncertainty quantification.
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.