Projection Embedded Diffusion Bridge for CT Reconstruction from Incomplete Data

2025-10-26

AI Summary

Inverse problems in incomplete-projection CT reconstruction are ill-posed, and existing diffusion bridge models struggle to effectively enforce data consistency, limiting image fidelity and fine-detail recovery. To address this, we propose a novel data-consistent diffusion bridge model: for the first time, the original incomplete projection measurements are directly embedded into the score function of the reverse diffusion process; measurement consistency is explicitly enforced via a tunable stochasticity parameter and an improved discretization scheme. We formulate a conditional diffusion framework governed by a projection-constrained stochastic differential equation (SDE), derive the posterior score analytically, and design a low-error numerical solver. Evaluated under three canonical incompleteness scenarios—sparse-view, limited-angle, and truncated projections—our method consistently outperforms state-of-the-art diffusion bridge approaches across standard, noisy, and domain-shifted settings, achieving both high-fidelity reconstructions and robust generalization.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Reconstructing CT images from incomplete projection data remains challenging due to the ill-posed nature of the problem. Diffusion bridge models have recently shown promise in restoring clean images from their corresponding Filtered Back Projection (FBP) reconstructions, but incorporating data consistency into these models remains largely underexplored. Incorporating data consistency can improve reconstruction fidelity by aligning the reconstructed image with the observed projection data, and can enhance detail recovery by integrating structural information contained in the projections. In this work, we propose the Projection Embedded Diffusion Bridge (PEDB). PEDB introduces a novel reverse stochastic differential equation (SDE) to sample from the distribution of clean images conditioned on both the FBP reconstruction and the incomplete projection data. By explicitly conditioning on the projection data in sampling the clean images, PEDB naturally incorporates data consistency. We embed the projection data into the score function of the reverse SDE. Under certain assumptions, we derive a tractable expression for the posterior score. In addition, we introduce a free parameter to control the level of stochasticity in the reverse process. We also design a discretization scheme for the reverse SDE to mitigate discretization error. Extensive experiments demonstrate that PEDB achieves strong performance in CT reconstruction from three types of incomplete data, including sparse-view, limited-angle, and truncated projections. For each of these types, PEDB outperforms evaluated state-of-the-art diffusion bridge models across standard, noisy, and domain-shift evaluations.

Problem

• Reconstructing CT images from incomplete projection data
• Incorporating data consistency into diffusion bridge models
• Improving reconstruction fidelity and detail recovery

Innovation

• Introduces projection embedded diffusion bridge model
• Uses reverse SDE conditioned on projection data
• Embeds projection data into score function