PFCM: Poisson flow consistency models for low-dose CT image denoising

TL;DR

This work addresses low-dose CT denoising by formulating posterior sampling for $p(m{x}|m{y})$ in a CT inverse problem and introducing Poisson Flow Consistency Models (PFCM) that distill PFGM++ into a single-step sampler with a tunable robustness parameter $D$. By adding a task-specific sampler that hijacks intermediate states with the observed LDCT image and optionally blends the result, PFCM achieves superior perceptual fidelity (LPIPS) and competitive structural similarity and PSNR on Mayo LDCT data, while maintaining robustness at small $D$ to mitigate noise-model mismatch. The method also demonstrates generalization to clinical PCCT data across energy levels. Compared with baselines including diffusion-based EDM, standard CM, and other denoising methods, PFCM delivers faster sampling and improved data fidelity, highlighting its practical impact for radiation-safe CT imaging and potential applicability to other medical inverse problems.

Abstract

X-ray computed tomography (CT) is widely used for medical diagnosis and treatment planning; however, concerns about ionizing radiation exposure drive efforts to optimize image quality at lower doses. This study introduces Poisson Flow Consistency Models (PFCM), a novel family of deep generative models that combines the robustness of PFGM++ with the efficient single-step sampling of consistency models. PFCM are derived by generalizing consistency distillation to PFGM++ through a change-of-variables and an updated noise distribution. As a distilled version of PFGM++, PFCM inherit the ability to trade off robustness for rigidity via the hyperparameter $D \in (0,\infty)$. A fact that we exploit to adapt this novel generative model for the task of low-dose CT image denoising, via a ``task-specific'' sampler that ``hijacks'' the generative process by replacing an intermediate state with the low-dose CT image. While this ``hijacking'' introduces a severe mismatch -- the noise characteristics of low-dose CT images are different from that of intermediate states in the Poisson flow process -- we show that the inherent robustness of PFCM at small $D$ effectively mitigates this issue. The resulting sampler achieves excellent performance in terms of LPIPS, SSIM, and PSNR on the Mayo low-dose CT dataset. By contrast, an analogous sampler based on standard consistency models is found to be significantly less robust under the same conditions, highlighting the importance of a tunable $D$ afforded by our novel framework. To highlight generalizability, we show effective denoising of clinical images from a prototype photon-counting system reconstructed using a sharper kernel and at a range of energy levels.

Figures (7)

• Figure 1: Overview of PFCM for the task of low-dose CT image denoising. The objective is to obtain a high-quality reconstruction $\bm{\hat{x}} \in \mathbb{R}^N$ of the normal dose CT image $\bm{x} \in \mathbb{R}^N$ based on the low-dose CT image $\bm{y}\in \mathbb{R}^N$. Approaching this as a statistical inverse problem, our solution is a sample $\hat{\bm{x}}$ from the posterior distribution $p(\bm{x}|\bm{y}).$ We enable sampling from said posterior by first training PFGM++ xu2023 in a supervised fashion to directly learn a mapping between the prior noise distribution and the posterior distribution of interest via the probability flow ODE by feeding the noisy image, $\bm{y}$, as additional input at training and test time. We subsequently obtain Poisson flow consistency models (PFCM) via consistency distillation song2023 using a change-of-variables and an updated noise distribution. A sample $\hat{\bm{x}}\sim p(\bm{x}|\bm{y})$ can then be obtained in a single-step as $\hat{\bm{x}}=f_{\bm{\theta}}(\bm{x}_\sigma,\bm{y},\sigma),$ for any intermediate $(\bm{x}_\sigma,\sigma)$, including for $\sigma_{\text{max}},$ where $\bm{x}_{\sigma_{\text{max}}}$ is pure noise. To adapt this setup for low-dose CT image denoising, where data fidelity is of utmost importance, we propose a "task-specific" sampler, which "hijacks" the sampling process, replacing the intermediate state $\bm{x}_{\sigma}$ with the low-dose CT image $\bm{y}$. Crucial to this approach is the robustness to "missteps" in the sampling process, afforded by PFCM via tunable $D \in (0,\infty)$.
• Figure 2: Ablation study of task-specific sampler: hijacking (h) + regularization (r). a) NDCT, b) LDCT, c) CM song2023, d) PFCM-262144, e) PFCM-2048, f) PFCM-128, g) CM+h, h) PFCM-262144+h, i) PFCM-2048+h, j) PFCM-128+h, k) CM+r, l) PFCM-262144+r, m) PFCM-2048+r, n) PFCM-128+r, o) CM+h+r, p) PFCM-262144+h+r, q) PFCM-2048+h+r, r) PFCM=128+h+r. Yellow circle added to emphasize lesion. Yellow arrow placed to emphasize detail. 1 mm-slices. Window setting [-160,240] HU.
• Figure 3: Results on the Mayo low-dose CT validation data. Abdomen image with a metastasis in the liver. a) NDCT, b) LDCT, c) BM3D makinen2020, d) RED-CNN chen2017, e) WGAN-VGG yang2018, f) EDM karras2022, g) PFGM++ xu2023, h) CM song2023. i) Proposed. Yellow box indicating ROI shown in Fig. \ref{['18_ex']}. 1 mm-slices. Window setting [-160,240] HU.
• Figure 4: ROI in Fig. \ref{['18']} magnified to emphasize details. a) NDCT, b) LDCT, c) BM3D makinen2020, d) RED-CNN chen2017, e) WGAN-VGG yang2018, f) EDM karras2022, g) PFGM++ xu2023, h) CM song2023, i) Proposed. Yellow circle added to emphasize lesion. Yellow arrow placed to emphasize detail. 1 mm-slices. Window setting [-160,240] HU.
• Figure 5: Absolute difference with respect to the NDCT image. a) LDCT, b) BM3D makinen2020, c) RED-CNN chen2017, d) WGAN-VGG yang2018, e) EDM karras2022, f) PFGM++ xu2023, g) CM song2023, h) Proposed. 1 mm-slices. Window setting [0,100] HU.