AutoStep: Locally adaptive involutive MCMC

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that AutoStep MCMC is $\pi$-invariant and has other desirable properties under mild assumptions on the target distribution $\pi$ and involutive proposal. Empirical results examine the effect of various step size selection design choices, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

XctDiff: Reconstruction of CT Images with Consistent Anatomical Structures from a Single Radiographic Projection Image

In this paper, we present XctDiff, an algorithm framework for reconstructing CT from a single radiograph, which decomposes the reconstruction process into two easily controllable tasks: feature extraction and CT reconstruction. Specifically, we first design a progressive feature extraction strategy that is able to extract robust 3D priors from radiographs. Then, we use the extracted prior information to guide the CT reconstruction in the latent space. Moreover, we design a homogeneous spatial codebook to improve the reconstruction quality further. The experimental results show that our proposed method achieves state-of-the-art reconstruction performance and overcomes the blurring issue. We also apply XctDiff on self-supervised pre-training task. The effectiveness indicates that it has promising additional applications in medical image analysis. The code is available at:https://github.com/qingze-bai/XctDiff