SONAR: A Structure-Consistent Neural Operator for Null-Space-Aware Sparse View CT Reconstruction

Song Ni; Haijun Yu; Haodong Li; Changsheng Fang; Shuyi Fan; Yixing Huang; Hengyong Yu

eess.IVSep 12, 2026

SONAR: A Structure-Consistent Neural Operator for Null-Space-Aware Sparse View CT Reconstruction

Authors: Song Ni, Haijun Yu, Haodong Li, Changsheng Fang, Shuyi Fan, Yixing Huang, Hengyong Yu

Organizations: Department of Electrical and Computer Engineering, University of Massachusetts Lowell, Lowell, MA 01854

Abstract

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.

Figures & tables

Fig. 1: Conceptual overview of SONAR. From left to right, the sinogram-domain A-UDNO predicts null-space-aware pseudo-measurements across different angular sampling densities; the dual-residual model independently characterizes uncertainties in the acquired measurements and learned pseudo-measurements; and the corresponding physics-lifted residuals are processed by re-discretizable image-domain UDNOs to impose structural consistency across reconstruction resolutions.

Fig. 2: Overall architecture of the proposed method. The pretrained A-UDNO first completes the full-view projection while preserving the measured views. At each cascade, the current reconstruction is forward projected and compared with the measured and learned complementary projections to form the range-space and null-space residuals, respectively. The two residuals are backprojected and processed by independent image-domain neural operators to update the reconstruction. The lower panel shows (a) the A-UDNO with anisotropic DISCO convolutions in the sinogram domain and (b) the image-domain UDNO based on standard DISCO convolutions.

Fig. 3: Qualitative comparison of sparse-view CT reconstruction methods on the AAPM dataset. Reconstructed images are displayed using a window of $[-1000,1000]$ HU, and the corresponding error maps are displayed within $[-100,100]$ HU. Red boxes indicate the regions of interest shown in the magnified insets

Fig. 4: error map of range-null space decomposition under the 47 views reconstruction on AAPM dataset. The display window is set to [-100,100] HU.

Fig. 5: Zero-shot cross-resolution reconstruction on the AAPM dataset. All models are trained at $256\times 256$ and directly evaluated at $384\times 384$ and $512\times 512$ without resolution-specific retraining. Error maps are displayed within $[-100,100]$ HU.

Setting	Views	Metric	FBP	CvG-Diff	CTO	MVMS-RCN	PAIL	SONAR
Seen	62	PSNR $\uparrow$	$31.55\pm 0.90$	$41.55\pm 1.26$	$43.40\pm 1.66$	$45.48\pm 1.01$	$47.01\pm 1.15$	$\mathbf{48.88\pm 1.64}$
		SSIM $\uparrow$	$0.7085\pm 0.0364$	$0.9768\pm 0.0064$	$0.9770\pm 0.0063$	$0.9837\pm 0.0036$	$0.9875\pm 0.0030$	$\mathbf{0.9908\pm 0.0029}$
		$\text{RMSE}_{\text{HU}}\downarrow$	$108.89\pm 11.24$	$34.63\pm 5.38$	$28.21\pm 5.73$	$21.94\pm 2.59$	$18.43\pm 2.54$	$\mathbf{15.00\pm 3.02}$
	47	PSNR $\uparrow$	$26.81\pm 0.72$	$40.73\pm 1.43$	$42.01\pm 1.73$	$44.91\pm 1.12$	$46.69\pm 1.76$	$\mathbf{47.05\pm 1.67}$
		SSIM $\uparrow$	$0.5211\pm 0.0485$	$0.9706\pm 0.0089$	$0.9705\pm 0.0081$	$0.9813\pm 0.0044$	$0.9856\pm 0.0054$	$\mathbf{0.9868\pm 0.0041}$
		$\text{RMSE}_{\text{HU}}\downarrow$	$187.73\pm 15.72$	$38.18\pm 6.68$	$33.15\pm 6.89$	$23.48\pm 3.10$	$19.40\pm 4.81$	$\mathbf{18.53\pm 3.71}$

TABLE I: Quantitative comparison under seen and unseen sparsity levels (Mean

\pm

Std). Symbol ∗ denotes sparsity levels not used during training and evaluated by direct zero-shot inference.

Resolution	Metric	CvG-Diff	CTO	MVMS-RCN	SONAR
$384\times 384$	PSNR $\uparrow$	$41.08\pm 1.22$	$39.40\pm 0.91$	$41.50\pm 1.19$	$\mathbf{44.60\pm 1.18}$
	SSIM $\uparrow$	$0.9575\pm 0.0129$	$0.9350\pm 0.0114$	$0.9365\pm 0.0189$	$\mathbf{0.9774\pm 0.0056}$
	$\text{RMSE}_{\text{HU}}\downarrow$	$36.56\pm 5.30$	$44.15\pm 4.62$	$34.78\pm 4.44$	$\mathbf{24.34\pm 3.40}$
$512\times 512$	PSNR $\uparrow$	$36.54\pm 0.53$	$37.63\pm 0.77$	$37.20\pm 1.05$	$\mathbf{45.26\pm 1.45}$
	SSIM $\uparrow$	$0.9206\pm 0.0167$	$0.9049\pm 0.0142$	$0.8718\pm 0.0428$	$\mathbf{0.9743\pm 0.0073}$
	$\text{RMSE}_{\text{HU}}\downarrow$	$61.09\pm 3.78$	$54.00\pm 4.78$	$56.97\pm 6.77$	$\mathbf{22.68\pm 3.87}$

TABLE II: Generalization and robustness evaluation across unseen image resolutions (Mean

\pm

Std).

Fig. 6: Visual comparison of different reconstruction methods on the clinical wrist dataset under sparse-view settings. The green box indicates the region of interest (ROI). Results are evaluated under both seen (93,62 views) and unseen (53 views) sampling conditions during training.

Views	Metric	FBP	CvG-Diff	CTO	MVMS-RCN	PAIL	SONAR	Energy Bin
93	PSNR $\uparrow$	$26.61\pm 0.25$	$32.68\pm 0.29$	$32.34\pm 0.31$	$32.66\pm 0.37$	$29.22\pm 0.22$	$\mathbf{34.11\pm 0.35}$	7-35keV
	SSIM $\uparrow$	$0.480\pm 0.005$	$0.713\pm 0.009$	$0.774\pm 0.012$	$0.648\pm 0.008$	$0.549\pm 0.006$	$\mathbf{0.783\pm 0.009}$
	RMSE $\downarrow$	$0.0467\pm 0.0014$	$0.0233\pm 0.0008$	$0.0242\pm 0.0009$	$0.0233\pm 0.0010$	$0.0346\pm 0.0009$	$\mathbf{0.0197\pm 0.0008}$
	PSNR $\uparrow$	$24.22\pm 0.20$	$30.27\pm 0.22$	$30.51\pm 0.23$	$30.16\pm 0.25$	$28.20\pm 0.16$	$\mathbf{31.54\pm 0.23}$	55-60keV
	SSIM $\uparrow$	$0.404\pm 0.004$	$0.601\pm 0.008$	$0.694\pm 0.006$	$0.506\pm 0.005$	$0.425\pm 0.003$	$\mathbf{0.727\pm 0.007}$
	RMSE $\downarrow$	$0.0615\pm 0.0014$	$0.0307\pm 0.0008$	$0.0298\pm 0.0008$	$0.0311\pm 0.0009$	$0.0389\pm 0.0007$	$\mathbf{0.0265\pm 0.0007}$

TABLE III: Quantitative comparison under different sparsity levels and energy bins (Mean

\pm

Std).

Fig. 7: Zero-shot cross-resolution reconstruction on the AAPM dataset. All models are trained at $256\times 256$ and directly evaluated at $384\times 384$ and $512\times 512$ without resolution-specific retraining.

Resolution	Metric	CvG-Diff	CTO	MVMS-RCN	SONAR
$384\times 384$	PSNR $\uparrow$	$25.24\pm 1.53$	$28.58\pm 1.62$	$24.98\pm 0.95$	$\mathbf{28.90\pm 1.54}$
	SSIM $\uparrow$	$0.507\pm 0.040$	$0.485\pm 0.066$	$0.345\pm 0.056$	$\mathbf{0.561\pm 0.053}$
	$\text{RMSE}\downarrow$	$0.0556\pm 0.0101$	$0.0379\pm 0.0073$	$0.0567\pm 0.0063$	$\mathbf{0.0365\pm 0.0067}$
$512\times 512$	PSNR $\uparrow$	$22.62\pm 1.56$	$25.90\pm 1.64$	$21.71\pm 0.83$	$\mathbf{26.31\pm 1.58}$
	SSIM $\uparrow$	$0.414\pm 0.026$	$0.377\pm 0.053$	$0.233\pm 0.034$	$\mathbf{0.457\pm 0.042}$
	$\text{RMSE}\downarrow$	$0.0752\pm 0.0143$	$0.0516\pm 0.0101$	$0.0825\pm 0.0080$	$\mathbf{0.0492\pm 0.0092}$

TABLE IV: Generalization and robustness evaluation across unseen image resolutions (Mean

\pm

Std).

Fig. 8: Effect of the number of cascades on reconstruction performance under the 62-, 47-, and 37-view settings. Performance improves progressively as the number of cascades increases and becomes nearly saturated at eight cascades.

Fig. 9: Ablation study of the anisotropic neural operator under different view settings.

Method	Testing time(s)	Parameters(M)
CTO	0.40	172
CvG_Diff	0.89	1.85
MVMS-RCN	0.05	0.29
PAIL	0.42	7.2
OURS	0.69	19.5

TABLE V: THE PARAMETER SIZE AND TEST TIME OF DIFFERENT METHODS WITH AN NVIDIA A6000 GPU

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