LDCT-to-SDCT as a Bridge Problem: Single-Step Residual Endpoint Flow Matching for Real-Time Denoising

Technical Summary: Residual Endpoint Flow Matching for LDCT Reconstruction

Problem Statement
Low-dose computed tomography (LDCT) reduces patient radiation exposure but introduces significant quantum noise and reconstruction artifacts, potentially obscuring low-contrast anatomical structures. While diffusion models have achieved high reconstruction quality by learning noise-to-image trajectories, their iterative sampling processes impose substantial computational costs, limiting their utility in real-time or latency-sensitive clinical applications. Existing adaptations often rely on sequential sampling that fails to fully exploit the specific nature of paired LDCT–standard-dose CT (SDCT) data. In paired scenarios, the target anatomy and spatial structure are already present in the LDCT input; the reconstruction task primarily involves correcting dose-related noise and artifacts rather than generating anatomical structures from scratch.

Methodology: Residual Endpoint Flow Matching (REFM)
The authors propose Residual Endpoint Flow Matching (REFM), a method that reframes LDCT reconstruction as a direct transport problem between paired endpoints rather than a generative noise-to-image process.

• Formulation: Instead of learning a stochastic trajectory from noise, REFM defines a deterministic linear path between an LDCT image ($x_L$) and its paired SDCT target ($x_H$). The conditional path is defined as $x_t = (1-t)x_L + tx_H$, where the conditional velocity is the constant endpoint residual ($x_H - x_L$).
• Training: A time-conditioned U-Net is trained to predict this residual velocity by minimizing the squared error between the predicted velocity and the true residual ($x_H - x_L$) across time-conditioned states along the interpolation path. This differs from direct residual regression, as the network observes intermediate states during training.
• Inference: Reconstruction is performed using Euler integration. The method supports both single-step ($K=1$) and multi-step ($K>1$) inference using the same trained network. For single-step inference, the reconstruction is simply $\hat{x}_H = x_L + v_\theta(x_L, 0)$.
• Model Architecture: The study evaluates five model variants (Base, Medium, Small, Mini, Tiny) with varying channel widths and residual depths, all operating on 256 $\times$ 256 single-channel images with time embeddings.

Key Contributions

1. Paired Conditional Flow Matching: A novel formulation specifically designed for LDCT reconstruction that learns the residual velocity along a direct linear path between aligned LDCT–SDCT pairs.
2. Systematic Evaluation: A comprehensive analysis of reconstruction quality and throughput across five model capacities and varying numbers of Euler steps (1 to 50).
3. Efficiency Breakthrough: Demonstration that diffusion-level reconstruction quality can be achieved with a single network evaluation, offering approximately 10$\times$ higher throughput compared to standard DDPM baselines.

Experimental Results
The models were evaluated on the TCIA Low-Dose CT dataset, with external generalization tested on the Mayo Clinic and Colorectal Liver Metastases (CRLM) datasets without fine-tuning.

• Single-Step Superiority: Contrary to typical diffusion models where more steps yield better quality, all REFM variants achieved their highest reconstruction quality with a single Euler step. Increasing steps to 50 resulted in decreased PSNR and throughput.
• Performance on TCIA: The REFM Base model achieved 50.98 dB PSNR and 0.9865 SSIM at 94.54 fps. This matches the quality of a 10-step DDPM (50.92 dB, 0.9847 SSIM) while operating at roughly 10.2$\times$ higher throughput (9.26 fps). The REFM Small variant offered a strong trade-off, achieving 50.71 dB PSNR at 198.56 fps.
• Anatomical Variations: Performance varied by anatomical region, with chest images presenting the most challenge. REFM Base outperformed DDPM-10 on chest images but showed slightly lower PSNR on liver and brain images, though SSIM remained comparable.
• Generalization:
  • Mayo Clinic: On paired quarter-dose data, REFM Base matched the performance of a 25-step DDPM (48.83 dB vs. 48.83 dB) with a single step.
  • CRLM: On synthetically degraded images, DDPM-25 maintained a performance advantage over REFM. However, REFM Small generalized better than the Base model in this setting, suggesting sensitivity to the specific degradation process.

Significance and Claims
The paper claims that exploiting the paired anatomical correspondence between LDCT and SDCT allows for diffusion-level reconstruction quality without the computational burden of iterative sampling. The primary significance lies in the ability to achieve high-fidelity denoising in a single network evaluation, making the approach suitable for real-time applications. The authors note that while REFM does not necessarily improve peak reconstruction quality beyond what is achievable by multi-step diffusion, it preserves this quality at a fraction of the sampling cost. The study concludes that this "bridge problem" formulation effectively reduces LDCT reconstruction to a single-step transport task, offering a promising step toward efficient, high-fidelity medical imaging in latency-sensitive settings. The authors acknowledge limitations, including the use of image-level metrics (PSNR/SSIM) rather than diagnostic fidelity and the exclusion of preprocessing overhead in throughput measurements.