Source-linked AI summary
CG-GLORE: A Conjugate Gradient-Based Global-Local Regularization Network for Sparse-View CT Reconstruction
Tran Xuan Hieu Le, Doanh C. Bui, Vu Trung Duong Le, Hoai Luan Pham, Khang Nguyen, Mai K. Nguyen, Tu Bao Ho, Yasuhiko Nakashima
TL;DR
Sparse-view CT reconstruction is ill-posed and prone to streak artifacts, while existing methods can rely on first-order updates or large regularization networks. CG-GLORE addresses this with CG-based structured-Hessian unrolling and GLORE global-local regularization, achieving improved reconstruction quality across AAPM and DeepLesion settings, particularly in highly ill-conditioned cases. Its Hessian treatment remains a second-order-inspired surrogate rather than an exact Newton method for the full learned objective.
Problem
Sparse-view CT lowers radiation dose but creates an ill-posed reconstruction problem with severe streak artifacts, while many existing designs use first-order updates or large regularization networks.
Method
CG-GLORE unfolds CG-solvable structured-Hessian updates with GLORE, which combines convolutional local modeling and sparse-patchified Nyström long-range representation.
Results
CG-GLORE improves reconstruction quality across AAPM and DeepLesion sparse-view and noise settings, especially in highly ill-conditioned cases.
Takeaways & Limitations
The framework offers an effective balance between model-based optimization and learned regularization for sparse-view CT reconstruction.
Takeaways & Limitations
The method uses an identity surrogate for learned-prior curvature rather than evaluating the exact Hessian of the full learned objective.
Abstract
from arXiv · showhide
Sparse-view computed tomography (CT) reduces radiation dose by acquiring fewer projection views, but the resulting inverse problem is highly ill-posed and often produces severe streak artifacts. Existing deep reconstruction methods have achieved promising performance, yet many rely on first-order updates or large regularization networks, which can be less effective in ill-conditioned settings. We propose \textbf{CG-GLORE}, a compact deep unrolling framework inspired by second-order optimization for sparse-view CT reconstruction. Each unrolled stage uses a CG-solved linear system based on a structured Hessian surrogate: it retains the physics-induced curvature of the data-fidelity term while using an identity approximation for the learned regularization term. Thus, the method is second-order-inspired rather than an exact Newton method for the full learned objective. To model image priors, we design a Global-Local Regularization Network (GLORE), which combines convolutional local feature extraction with a Long-Range Dependency Representation module based on sparse patchification and Nyström attention. This design captures anatomical details and non-local dependencies while maintaining practical complexity. Experiments on AAPM and DeepLesion under multiple sparse-view and noise settings show that CG-GLORE achieves strong quantitative performance, stable convergence, lower noise power, and improved visual fidelity compared with representative reconstruction methods.
Introduction
Sparse-view CT lowers radiation dose but makes reconstruction highly ill-posed, motivating compact physics-aware unrolling with stronger optimization and global-local image priors.
- Motivation: Sparse-view CT reduces projection views and radiation dose but often causes severe streak artifacts because incomplete measurements make reconstruction highly ill-posed.FBP is especially vulnerable to these artifacts.
- Motivation: Existing deep unrolling methods embed iterative optimization but commonly use first-order updates and large regularization networks for ill-conditioned reconstruction.Earlier deep methods may also remain weakly coupled to reconstruction physics and rely heavily on local image statistics.
- CG-GLORE: CG-GLORE uses a structured Hessian surrogate and Conjugate Gradient to provide compact, physics-aware, second-order-inspired stage updates.The surrogate retains data-fidelity curvature while approximating the learned regularization term with the identity.
- GLORE: GLORE combines convolutional local feature extraction with Nyström-based long-range dependency modeling through sparse patchification.Its design targets anatomical details and non-local structure while maintaining compactness and practical complexity.
- Evaluation: CG-GLORE is validated across sparse-view and noise settings, showing improved reconstruction quality and favorable optimization behavior.The supplied introduction states this validation broadly without reporting a specific metric here.
2 Related Work
Related work progresses from image-domain FBP enhancement to dual-domain and deep-unrolled reconstruction, but data consistency and physics coupling remain concerns under sparse or noisy acquisition.
- Image-domain methods: Early sparse-view CT methods enhance FBP reconstructions with convolutional networks that suppress streak artifacts and recover anatomical structures.These approaches treat reconstruction primarily as an image-restoration task.
- Dual-domain methods: Dual-domain methods incorporate sinogram information to interpolate or refine projection data before or during image reconstruction.They extend image-domain restoration by exploiting the measurement process.
- Limitations: Despite promising visual quality, these approaches may remain weakly coupled to the optimization model and struggle to enforce data consistency under highly sparse or noisy acquisition.The passage frames this as a limitation of the related approaches rather than a universal failure.
3 Methodology
CG-GLORE reconstructs sparse-view CT images through CG-based unrolled optimization and a global-local regularization network. Its design combines physics-aware curvature modeling with local and long-range feature processing while reducing attention complexity through sparse patchification and Nyström approximation.
- Problem formulation: The inverse problem reconstructs a CT image from incomplete sinogram measurements using an iterative objective with data fidelity and regularization terms.The forward model includes the Radon transform and measurement noise, while sparse-view acquisition reduces the available projection views.
- Second-order-inspired update: CG-GLORE replaces conventional first-order updates with a CG-solved linear system based on a structured Hessian surrogate.The surrogate retains analytic data-fidelity curvature, approximates learned-regularization curvature by identity, and avoids explicit inverse computation.
- Global-local regularization: GLORE approximates the learned regularization gradient using convolutional layers for local patterns and LORAD for relationships between distant image regions.The architecture places LORAD between an initial convolution and two subsequent convolutions; its feature map is patchified into tokens before global processing.
- Efficient tokenization: Sparse patchification compresses spatial information into channels, reducing the token count from N to N/k2 and attention complexity from O(N2) to O(N2/k4).Dilated, non-overlapping patches group distant spatial values while preserving essential structural information.
- Long-range dependency representation: Nyström attention approximates long-range token relationships with L landmarks, reducing attention computation from O(˜N2) to O(˜N).The approximation uses low-rank decomposition and the Moore-Penrose pseudoinverse, followed by multi-head processing.
- Design rationale: The structured surrogate yields a symmetric positive definite system suitable for CG while separating optimization updates from learned image-prior modeling.CG supplies update directions, whereas GLORE models image regularity without explicitly representing the full learned-objective curvature.
Experiments
Experiments on AAPM and DeepLesion evaluate CG-GLORE across sparse-view, noise, convergence, noise-power, visual-quality, efficiency, and ablation settings. The results show strong reconstruction quality, stable behavior, reduced residual noise, and a compact computational profile.
- Datasets and settings: CG-GLORE is evaluated on AAPM and DeepLesion using multiple sparse-view and noise configurations, with AAPM split into training, validation, and testing patients.AAPM uses 2,378 images from 10 patients; DeepLesion contains images from 4,427 patients.
- Quantitative results: 42.05/97.59, 47.66/99.05, and 52.43/99.62 PSNR/SSIM are achieved on AAPM with 32, 64, and 128 views in the noiseless setting.The 32-view result exceeds the second-best method by 1.53 dB PSNR.
- Convergence: At 50 epochs, CG-GLORE outperforms the strongest plotted baseline by 1.35 dB, 0.50 dB, and 0.33 dB in PSNR, while gains from 40 to 50 epochs are at most 0.07 dB PSNR and 0.03 SSIM.These values indicate strong plotted performance and small late-stage changes.
- Noise-power analysis: CG-GLORE achieves the lowest residual NPS over the full radial-frequency range in the 32-view setting and remains among the lowest curves with 64 views.The NPS analysis uses fixed 32×32 ROIs, totaling 57 ROIs per image.
- Computational efficiency: CG-GLORE uses 15 reconstruction iterations and 5.5M parameters, requiring fewer iterations than LEARN and DPMA while retaining stronger reconstruction accuracy than lightweight Learned PD.The comparison is conducted on AAPM with 32 views.
- Qualitative results: Visual comparisons show fewer streak artifacts, clearer soft-tissue structures, sharper lung vessels, better local-edge preservation, and weaker residual patterns than competing methods.The comparisons cover 32 projections with low noise and 64 projections without noise.
- Ablation studies: Ablations show that GLORE improves first-order reconstruction from 36.02 to 40.09 PSNR and from 92.94 to 96.63 SSIM, while CG iterations further improve the surrogate update.The default solver depth is ten CG iterations, balancing reconstruction quality and solver cost.
5 Conclusion
CG-GLORE combines a CG-solvable structured Hessian surrogate with GLORE for sparse-view CT reconstruction. Experiments show improved quality in highly ill-conditioned settings, while future work targets broader clinical and 3D validation.
- CG-GLORE uses a CG-solvable structured Hessian surrogate that retains data-fidelity curvature while approximating learned regularization with the identity.It is second-order-inspired rather than an exact Newton method for the full learned objective.
- GLORE combines convolutional local modeling with efficient long-range dependency representation.
- Experiments on AAPM and DeepLesion show improved reconstruction quality, particularly in highly ill-conditioned settings.Ablations support complementary contributions from the CG solver and GLORE.
- CG-GLORE balances model-based optimization and learned regularization for sparse-view CT reconstruction.
- Future work will examine broader validation on real clinical acquisition protocols and extension to more general 3D reconstruction settings.