PPFM: Image denoising in photon-counting CT using single-step posterior sampling Poisson flow generative models

Abstract: Diffusion and Poisson flow models have shown impressive performance in a wide range of generative tasks, including low-dose CT image denoising. However, one limitation in general, and for clinical applications in particular, is slow sampling. Due to their iterative nature, the number of function evaluations (NFE) required is usually on the order of $10-10^3$, both for conditional and unconditional generation. In this paper, we present posterior sampling Poisson flow generative models (PPFM), a novel image denoising technique for low-dose and photon-counting CT that produces excellent image quality whilst keeping NFE=1. Updating the training and sampling processes of Poisson flow generative models (PFGM)++, we learn a conditional generator which defines a trajectory between the prior noise distribution and the posterior distribution of interest. We additionally hijack and regularize the sampling process to achieve NFE=1. Our results shed light on the benefits of the PFGM++ framework compared to diffusion models. In addition, PPFM is shown to perform favorably compared to current state-of-the-art diffusion-style models with NFE=1, consistency models, as well as popular deep learning and non-deep learning-based image denoising techniques, on clinical low-dose CT images and clinical images from a prototype photon-counting CT system.