Evaluating the Posterior Sampling Ability of Plug&Play Diffusion Methods in Sparse-View CT

TL;DR

The paper tackles the challenge of evaluating posterior sampling by Plug&Play diffusion models for Sparse-View CT, where the posterior $p(\mathbf{x}|\mathbf{y}_p)$ can be multimodal due to very few projections. It introduces two evaluation criteria, Posterior-Prior Similarity (PPS) and Normalized Measurement Consistency (NMC), and conducts a large-scale quantitative study across three datasets using three SOTA PnP methods (MCG, DPS, $\Pi$G) over multiple projection counts $p$. The results reveal that all methods' approximate posteriors diverge from the true posterior as $p$ decreases, with DPS generally closest to the true posterior yet still imperfect, while $\Pi$G largely ignores the conditioning. These findings highlight the limitations of current posterior-sampling approaches under extreme sparsity and underscore the need for posterior-aware evaluation beyond traditional image-quality metrics, guiding future improvements in SVCT reconstruction with generative models.

Abstract

Plug&Play (PnP) diffusion models are state-of-the-art methods in computed tomography (CT) reconstruction. Such methods usually consider applications where the sinogram contains a sufficient amount of information for the posterior distribution to be concentrated around a single mode, and consequently are evaluated using image-to-image metrics such as PSNR/SSIM. Instead, we are interested in reconstructing compressible flow images from sinograms having a small number of projections, which results in a posterior distribution no longer concentrated or even multimodal. Thus, in this paper, we aim at evaluating the approximate posterior of PnP diffusion models and introduce two posterior evaluation properties. We quantitatively evaluate three PnP diffusion methods on three different datasets for several numbers of projections. We surprisingly find that, for each method, the approximate posterior deviates from the true posterior when the number of projections decreases.

Figures (1)

• Figure 1: Top row: two compressible flow posterior samples from a PnP diffusion model chung2023diffusion using the same measured sinogram $\mathbf{y}_6$, i.e. $p\text{\,=\,}6$. The two samples look very different because the posterior is not peaked when the sinogram contains few projections. Bottom: histograms of 10000 posterior samples chung2023diffusion of the red boxed pixel location $\mathbf{x}_i$, for $p\text{\,=\,}6, 12 \text{ and } 30$ projections. When $p\text{\,=\,}6$ the posterior is not peaked anymore, thus a point estimation of $\mathbf{x}$ is not sufficient and being able to properly sample from the true posterior is fundamental, which we evaluate in this paper.