Towards Prospective Medical Image Reconstruction via Knowledge-Informed Dynamic Optimal Transport

TL;DR

This work tackles prospective medical image reconstruction by reframing the problem as a dynamic transport from the measurement distribution to a distribution of high-quality images. It introduces imaging Knowledge-Informed Dynamic Optimal Transport (KIDOT), which integrates imaging physics into both the instantaneous data-fidelity cost $c(x,y)=\|y-\mathcal{A}(x)\|_1$ and the transport dynamics via a gradient-flow equation $\frac{\mathrm{d} I_t}{\mathrm{d}t}= -\big(\mathcal{A}^*(\mathcal{A}(I_t) - I_0) + \nabla \mathcal{R}(I_t)\big)$. The authors provide a neural-network-based implementation that learns from unpaired data, derives a tractable training objective combining a KIDOT loss with a supervised term when paired data are available, and prove the existence of minimizers under standard assumptions. Extensive experiments on simulated MRI, real prospective MRI, and clinical LDCT demonstrate that KIDOT achieves superior fidelity and perceptual metrics, while remaining robust to distribution shifts and misalignment, highlighting its potential for practical clinical deployment. The framework offers a data-efficient, physics-consistent alternative to purely data-driven or static OT approaches for prospective reconstruction tasks.

Abstract

Medical image reconstruction from measurement data is a vital but challenging inverse problem. Deep learning approaches have achieved promising results, but often requires paired measurement and high-quality images, which is typically simulated through a forward model, i.e., retrospective reconstruction. However, training on simulated pairs commonly leads to performance degradation on real prospective data due to the retrospective-to-prospective gap caused by incomplete imaging knowledge in simulation. To address this challenge, this paper introduces imaging Knowledge-Informed Dynamic Optimal Transport (KIDOT), a novel dynamic optimal transport framework with optimality in the sense of preserving consistency with imaging physics in transport, that conceptualizes reconstruction as finding a dynamic transport path. KIDOT learns from unpaired data by modeling reconstruction as a continuous evolution path from measurements to images, guided by an imaging knowledge-informed cost function and transport equation. This dynamic and knowledge-aware approach enhances robustness and better leverages unpaired data while respecting acquisition physics. Theoretically, we demonstrate that KIDOT naturally generalizes dynamic optimal transport, ensuring its mathematical rationale and solution existence. Extensive experiments on MRI and CT reconstruction demonstrate KIDOT's superior performance.

Figures (12)

• Figure 1: (a) Core concept of KIDOT: modeling image reconstruction as a continuous evolution from a prospective degraded distribution $\mathbb{P}$ to a high quality image distribution $\mathbb{Q}$, guided by dynamic OT. (b) The retrospective-prospective gap in MRI: a visual comparison of k-space data from retrospective simulations versus real prospective undersampling (top), and their corresponding k-space reconstructions via supervised learning (bottom).
• Figure 2: Illustration of the KIDOT framework. KIDOT employs a sequence of transformations $T_{\phi}^{t_i}$, governed by a learned transport equation driven by the medical image reconstruction model, to map measurement $y$ from the prospective degraded domain to the reconstructed domain. The transport process is guided by the KIDOT objective function, which critically incorporates imaging knowledge by enforcing data consistency along the transport path. Simultaneously, it promotes distribution matching between the reconstructed domain and the target high-quality domain using potentials $\varphi_{\theta}$.
• Figure 3: Qualitative comparison of MR reconstruction methods on the prospectively acquired United Imaging brain dataset (T2-FLAIR, 10x acceleration). KIDOT demonstrates enhanced detail recovery (e.g., red box).
• Figure 4: Qualitative results for LDCT reconstruction on clinical prospective data. Comparison illustrates noise reduction and detail enhancement achieved by KIDOT.
• Figure 5: (a) Visualization of simulated images: the first column shows fully sampled images, the second column is used for supervised learning, the third column represents the undersampled prospective data, and the fourth column shows the residuals (difference between supervised and prospective images). (b) Visualization of simulated images:the first row is the retrospective mask, and the second row is the prospective mask.

Theorems & Definitions (4)

• Theorem 3.1: Existence and Geometry of Minimizer for $L^2$ Distance Integral
• Theorem 3.2: Existence of Minimizer for KIDOT Objective
• Theorem A.1: Existence and Geometry of Minimizer for $L^2$ Distance Integral
• Theorem A.2: Existence of Minimizer for KIDOT Objective