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

cs.CVAug 15, 2026

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

Abstract

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 $x_{0}$ , 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						$N_{G}$ = 5%, $N_{P}$ = $10^{6}$						$N_{G}$ = 5%, $N_{P}$ = $5\times 10^{5}$
	$n_{view}$ = 32		$n_{view}$ = 64		$n_{view}$ = 128		$n_{view}$ = 32		$n_{view}$ = 64		$n_{view}$ = 128		$n_{view}$ = 32		$n_{view}$ = 64		$n_{view}$ = 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				$N_{G}$ = 5%, $N_{P}$ = $10^{6}$				$N_{G}$ = 5%, $N_{P}$ = $5\times 10^{5}$
	$n_{view}$ = 18		$n_{view}$ = 32		$n_{view}$ = 18		$n_{view}$ = 32		$n_{view}$ = 18		$n_{view}$ = 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.

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

n_{\text{view}}=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 ( $N_{P}=5\times 10^{5}$ ), visualized in the HU window $[-1000,700]$ .

Table 9

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Sparse-View CT Reconstruction Image Inverse Problems Neural Operators

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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 1.87~~dB at 62 views and by 7.63~~dB under zero-shot transfer to a

512\times512

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.

Abstract

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