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.

一种使用深度生成先验进行贝叶斯推断的新方法，该方法通过引入具有自注意力结构的双向生成对抗网络的SA-Roundtrip先验，在低维潜在空间中应用具有预条件Crank-Nicolson算法的Hamiltonian Monte Carlo对后验分布进行推断，以实现可控采样生成并确定数据的内在维度。在计算机断层扫描重构中进行的实验结果表明，该方法优于当前最先进的方法，始终产生精确的点估计并提供准确的不确定性量化。

基于HMC-pCN采样方法的带有SA-Roundtrip先验的贝叶斯成像反问题