Geometry-Aware Diffusion Approximate Posterior Sampling for Sparse-View and Limited-Angle CT

2026-10-05

AI Summary

This study addresses the blurring and artifacts arising from missing directional information in sparse-view and limited-angle CT reconstruction by proposing a geometry-aware diffusion stochastic reconstruction framework. For the first time, this framework introduces continuously varying measurement sensitivity, adaptively modulating reconstruction updates and stochastic exploration via a noise-weighted pullback metric. By integrating matrix-free projection operators, conjugate gradient solvers, and data consistency corrections, it overcomes the limitations of conventional fixed likelihood guidance and null-space correction approaches. Experimental results demonstrate that the proposed method achieves high-fidelity reconstruction with strong measurement consistency across diverse CT scenarios, while simultaneously generating spatially resolved empirical uncertainty estimates.

Abstract

Sparse-view computed tomography (CT) reduces radiation dose and acquisition time and may mitigate motion artifacts. However, angular undersampling provides insufficient information to determine the image uniquely and stably. Limited-angle CT, arising from restricted angular coverage, produces strongly directional information loss associated with the missing angular range. In both settings, image directions may be strongly observed, weakly constrained, or unobservable, leading to severe ill-posedness and reconstruction ambiguity. Existing diffusion-based approaches incorporate measurement information through likelihood guidance, data-consistency operations, or range-null-space corrections. However, they do not generally use the continuously varying measurement sensitivity of the acquisition to jointly shape both reconstruction updates and stochastic exploration. We propose a geometry-aware diffusion-guided stochastic reconstruction framework for sparse-view and limited-angle CT. Its central component is a regularized noise-weighted pullback metric constructed from the CT forward operator and measurement-noise covariance. This metric continuously adapts both the measurement-aware update and stochastic exploration according to directional measurement sensitivity, suppressing changes along strongly constrained directions while permitting greater exploration along weakly constrained and unobservable directions. We complement this geometry-aware update with a regularized data-consistency correction and approximately null-space-restricted stochastic perturbations, implemented matrix-free using forward and backprojection operations together with conjugate-gradient solves. Experiments on sparse-view, noisy, and limited-angle CT demonstrate competitive reconstruction quality, strong measurement consistency, and spatially resolved empirical uncertainty estimates.

Problem

• Sparse-view CT
• Limited-angle CT
• Ill-posedness
• Reconstruction ambiguity
• Diffusion models

Innovation

• Geometry-aware diffusion
• Sparse-view CT
• Pullback metric
• Null-space perturbation
• Uncertainty estimation