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

TL;DR

This paper evaluates the ability of Plug&Play diffusion models to approximate the true posterior distribution in sparse-view CT reconstruction, revealing deviations as the number of projections decreases.

Contribution

It introduces two properties for evaluating the posterior and assesses three PnP diffusion methods across multiple datasets with varying projections.

Findings

Approximate posteriors deviate from true posteriors with fewer projections

Evaluation introduces new properties for posterior assessment

Surprising deviations observed in all tested methods

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.