CG-GLORE: A Conjugate Gradient-Based Global-Local Regularization Network for Sparse-View CT Reconstruction
Authors: Tran Xuan Hieu Le, Doanh C. Bui, Vu Trung Duong Le, Hoai Luan Pham, Khang Nguyen, Mai K. Nguyen, Tu Bao Ho, Yasuhiko Nakashima
Organizations: Nara Institute of Science and Technology Nara, Japan · University of Information Technology Ho Chi Minh City, Vietnam · Vietnam National University Ho Chi Minh City, Vietnam · ETIS, CY Cergy Paris University, ENSEA, CNRS, UMR 8051 Cergy-Pontoise, France · Vietnam Institute for Advanced Study in Mathematics Hanoi, Vietnam
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.
Figures & tables
Figure 1: Overview of the proposed CG-GLORE framework. Starting from an FBP reconstruction x0 , CG-GLORE performs T unrolled reconstruction iterations. At each iteration, a Conjugate Gradient solver computes an update from the structured Hessian surrogate, while the global-local regularization network captures local structures and long-range dependencies to further refine the reconstruction.
Method
No noise
NG = 5%, NP = 106
NG = 5%, NP = 5×105
nview = 32
nview = 64
nview = 128
nview = 32
nview = 64
nview = 128
nview = 32
nview = 64
nview = 128
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
FBPConvNet [ 10 ]
31.33
87.02
38.42
94.02
42.97
97.46
31.52
83.37
37.35
94.32
42.06
97.34
31.28
86.6
36.81
93.57
41.23
96.83
LearnedPD [ 2 ]
40.7
97.07
47.04
98.95
51.62
99.56
39.59
96.27
43.87
98.2
45.72
98.7
39.07
96.07
42.81
97.83
44.49
98.39
LEARN [ 5 ]
40.52
96.78
47.65
99.04
50.52
99.47
40.04
96.56
44.09
98.24
45.82
98.71
39.53
96.25
42.98
97.88
44.58
98.4
QN-Mixer † [ 3 ]
39.51
96.11
45.57
98.48
50.09
99.32
37.50
94.92
42.46
97.70
44.27
98.11
35.91
92.49
38.73
94.92
40.51
96.27
Table 1: Quantitative comparison between CG-GLORE and state-of-the-art methods on the AAPM dataset. The best and second-best results are highlighted in red (bold) and yellow (underlined), respectively.
Method
No noise
NG = 5%, NP = 106
NG = 5%, NP = 5×105
nview = 18
nview = 32
nview = 18
nview = 32
nview = 18
nview = 32
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
FBPConvNet [ 10 ]
28.72
69.2
32.76
84.89
29.27
79.77
32.21
82.27
29.1
78.53
32.74
84.46
LearnedPD [ 2 ]
34.82
92.34
39.90
96.50
34.65
92.23
39.37
96.14
34.54
92.04
39.09
96.00
DPMA [ 28 ]
31.92
84.73
35.34
89.53
31.81
83.69
35.09
88.25
31.73
83.23
34.76
87.34
RegFormer [ 29 ]
35.64
92.49
40.71
96.81
35.48
92.05
40.16
96.55
35.39
92.19
39.80
96.33
Table 2: Performance comparison between CG-GLORE and other state-of-the-art methods on DeepLesion dataset.
Figure 2: Convergence analysis on the AAPM dataset. PSNR and SSIM are plotted as functions of training epochs for different reconstruction methods. Each curve consists of five evaluation points corresponding to 10, 20, 30, 40, and 50 training epochs, highlighting the convergence speed and stability of the compared methods.
Figure 5
Method
#Iters
Params (M)
Mem. (GB)
FBPConvNet [ 10 ]
-
31.1
1.51
Learn PD [ 2 ]
10
0.251
0.75
LEARN [ 5 ]
30
1.8
1.41
QN-Mixer † [ 3 ]
14
8.5
7.83
RegFormer [ 29 ]
10
2.7
5.79
DPMA [ 28 ]
300
8.1
7.78
Table 3: Computational efficiency comparison of sparse-view CT reconstruction methods trained on AAPM with nview=32 .
Figure 5: Visual comparison on the AAPM dataset. The figure presents reconstructed CT images and their corresponding difference maps under different acquisition settings. Top row: sparse-view reconstruction with 32 projections and low noise level, visualized in the HU window [−200,300] . Bottom row: reconstruction with 64 projections without noise, visualized in the HU window [−1000,700] .
Figure 6: Stage-wise reconstruction evolution of CG-GLORE. Intermediate reconstructions are shown under 32 projection views and a high-noise setting ( NP=5×105 ), visualized in the HU window [−1000,700] .
Sparse-view computed tomography (CT) reduces radiation dose and acquisition time but remains severely ill-posed because incomplete projections poorly constrain null-space information. Existing learning-based methods often estimate this information in high-dimensional image space, conflate physical measurement errors with prediction errors, and depend on fixed discretizations. We propose SONAR, a Structure-Consistent Neural Operator for Null-Space-Aware Reconstruction. Instead of recovering the full null-space component, SONAR predicts a low-dimensional null-space-aware representation from the acquired projections as pseudo-measurements. It separates measurement and pseudo-measurement residuals, lifts them into the image domain through physics operators, and applies independent neural operators to constrain their structural effects, thereby accommodating admissible errors while suppressing unsupported structures. To support cross-discretization reconstruction, an anisotropic U-shaped neural operator models the periodic angular and nonperiodic detector dimensions using direction-dependent continuous supports, while image-domain neural operators re-discretize continuous kernels on target grids. These components form an optimization-inspired unrolled network. Experiments on simulated AAPM and clinical MARS photon-counting CT data demonstrate consistent improvements across seen and unseen view settings and unseen image resolutions. On AAPM dataset, SONAR improves PSNR by 1.87dB at 62 views and by 7.63dB under zero-shot transfer to a 512×512 grid over the strongest competing methods. SONAR also achieves the best overall performance in all clinical settings evaluated, demonstrating accurate, structurally reliable, and discretization-robust sparse-view CT reconstruction.
Song Ni, Haijun Yu, Haodong Li +4
Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA 01854
Sparse-view CT reduces radiation dose and scanning time by acquiring fewer projection views, but angular undersampling makes reconstruction severely ill-posed, causing streak artifacts, structural blurring, and loss of fine details. Existing supervised methods are often tied to specific sampling settings, whereas generative methods may introduce anatomically inconsistent hallucination-like structures under severe undersampling. We propose Lucid, a sparsity-adaptive, consistency-guided reconstruction framework based on a Flow Matching generative prior for sparse-view CT. Lucid is trained only on high-quality CT images to learn a continuous transport between a Gaussian distribution and the high-quality CT image distribution, independent of view sampling. During inference, the sampling sparsity level is explicitly incorporated to adapt the generative trajectory of a single pretrained model. Specifically, Lucid constructs a degradation-matched initial state by sparsity-weighted fusion of the sparse-view FBP image and Gaussian noise, performs sparsity-modulated Flow Matching updates, and applies projection-domain data-consistency correction after each prior update. Experiments under multiple sparse-view settings show that Lucid achieves stable reconstruction performance across different sampling densities, improves image quality and structural fidelity, and reduces the risk of hallucination-like structures in generative sparse-view CT reconstruction.
Jigang Duan, Jiayi Wang, Heran Wang +3
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China · National Center for Applied Mathematics Beijing, Capital Normal University and Academy for multidisciplinary studies, Capital Normal University, Beijing, 100048, China
A long-term goal in CT imaging is to achieve fast and accurate 3D reconstruction from sparse-view projections, thereby reducing radiation exposure, lowering system cost, and enabling timely imaging in clinical workflows. Recent feed-forward approaches have shown strong potential toward this overarching goal, yet their results still suffer from artifacts and loss of fine details. In this work, we introduce Iterative Latent Volumes (ILV), a feed-forward framework that integrates data-driven priors with classical iterative reconstruction principles to overcome key limitations of prior feed-forward models in sparse-view CBCT reconstruction. At its core, ILV constructs an explicit 3D latent volume that is repeatedly updated by conditioning on multi-view X-ray features and the learned anatomical prior, enabling the recovery of fine structural details beyond the reach of prior feed-forward models. In addition, we develop and incorporate several key architectural components, including an X-ray feature volume, group cross-attention, efficient self-attention, and view-wise feature aggregation, that efficiently realize its core latent volume refinement concept. Extensive experiments on a large-scale dataset of approximately 14,000 CT volumes demonstrate that ILV significantly outperforms existing feed-forward and optimization-based methods in both reconstruction quality and speed. These results show that ILV enables fast and accurate sparse-view CBCT reconstruction suitable for clinical use. The project page is available at: https://sngryonglee.github.io/ILV/.