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Efficient Flow Matching for Sparse-View CT Reconstruction

Jiayang Shi, Lincen Yang, Zhong Li, Tristan Van Leeuwen, Daniel M. Pelt, K. Joost Batenburg

TL;DR

An FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency.

Abstract

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.

Efficient Flow Matching for Sparse-View CT Reconstruction

TL;DR

An FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency.

Abstract

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at https://github.com/EFMCT/EFMCT.
Paper Structure (6 sections, 1 theorem, 24 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 6 sections, 1 theorem, 24 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Method
  3. Results
  4. Conclusion
  5. Appendix: Proof of Proposition \ref{['prop:reuse']}
  6. Appendix: Algorithm

Key Result

proposition 1

Assume that $\bm{v}$ is locally Lipschitz in both $\bm{x}$ and t. Then, for a single reuse step, the local deviation between the reuse update $\hat{\bm{x}}_{k+1}$ and the standard Euler update $\bm{x}_{k+1}$ satisfies i.e., velocity reuse introduces a local error of the same order as the Euler discretization itself. Moreover, if the same velocity is reused for at most $M$ consecutive steps (indep

Figures (4)

  • Figure 1: Left: Cosine similarity of predicted velocity fields at consecutive iterations in FMCT, with and without data consistency correction, showing strong correlation across adjacent steps. Right: Reconstruction performance vs. NFE for DM methods and FMCT/EFMCT, demonstrating that FMCT/EFMCT achieve competitive quality at substantially lower NFEs. DM methods here use the deterministic DDIM sampler for fairness; DPS/MCG results with the original 1000-step DDPM sampler are shown as isolated points. Results are averaged over the same randomly selected 21 reconstructions from the AAPM dataset across all iteration settings; shaded regions indicate standard deviation.
  • Figure 2: Overview of our proposed FMCT(left) and EFMCT(right) method.
  • Figure 3: Visual comparison of reconstructions across different methods, datasets, and views. PSNR, SSIM, and reconstruction time are shown in the lower-left, lower-right, and upper-right corners of each image, respectively. We visualize only the best three diffusion-based methods for better visibility. Zoom in for more details.
  • Figure 4: Ablation of the velocity reuse strategy. Left: Reuse enabled after different iteration indices. Right: Varying the maximum number of consecutive reuse steps. Shaded regions indicate standard deviation.

Theorems & Definitions (2)

  • proposition 1
  • proof