LINGO: Latent Initialization and Gradient Optimization for Sparse-view X-ray Novel View Synthesis and CT Reconstruction with 3D Gaussian Splatting

Lifeng Xing; Dequan Jin; Kunpeng Bu; Peigeng He; Shihui Ying

cs.CVSep 19, 2026

LINGO: Latent Initialization and Gradient Optimization for Sparse-view X-ray Novel View Synthesis and CT Reconstruction with 3D Gaussian Splatting

Authors: Lifeng Xing, Dequan Jin, Kunpeng Bu, Peigeng He, Shihui Ying

Organizations: School of Mathematics and Center for Applied Mathematics of Guangxi, Guangxi University, Nanning 530004, China · Department of Endocrinology, Metabolism and Nephrology, Guangxi Medical University Cancer Hospital, Nanning 530021, China · School of Mechanics and Engineering Science and Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China

Abstract

In novel view synthesis and Computed Tomography (CT) reconstruction with sparse-view X-ray imaging, insufficient angular coverage leads to structural ambiguity and accumulated noise. Integrating 3D Gaussian Splatting (3DGS) with X-ray absorption physics can achieve promising results, but it suffers from noisy initialization, positional insensitivity, and weak gradients in low-density regions. In this paper, we propose a unified Latent Initialization and Gradient Optimization (LINGO) framework to address these issues. LINGO combines latent mask-space initialization with dynamic gradient optimization to improve point cloud structural completeness while accelerating training. It constructs voxel-level 3D filters from X-ray masks to robustly suppress background noise and provide reliable geometric priors. By employing an adaptive voxel scaling strategy and dynamically scaling loss, LINGO can adjust spatial resolution and explicitly amplify gradients in low-density structures. To evaluate the quality of initialization, we introduce the Initialization Point Cloud Structural Deviation (IPSD) metric. Experiments on the X3D dataset indicate that for the novel view synthesis task, LINGO improves the Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) by an average of 0.72 and 0.0039, respectively, over baselines under identical sparse-view settings, achieving comparable reconstruction quality within 5k steps to state-of-the-art models typically trained with 30k iterations. For the CT reconstruction task, LINGO also demonstrates consistent improvements, with average PSNR and SSIM gains of 0.36 and 0.0134. These results highlight LINGO's effectiveness in both accelerating training and enhancing reconstruction quality across different sparse-view imaging scenarios.

Figures & tables

Fig. 1: Overview of the proposed LINGO framework. (a) Overall training pipeline of LINGO with $\text{R}^{2}$ -Gaussian backbone. (b) LINGO initialization module for mask-guided Gaussian point generation. (c) Mask detection and filtering submodule within the initialization stage.

View Num	Iter	3DGS			X-Gaussian			$\text{R}^{2}$ -Gaussian			LINGO
View Num	Iter	PSNR $\uparrow$	SSIM $\uparrow$	IPSD $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	IPSD $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	IPSD $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	IPSD $\downarrow$
5	5k	28.74	0.8871	0.1241	28.88	0.8899	0.1236	32.90	0.9449	0.1228	33.33	0.9506	0.0282
	15k	28.55	0.8887	0.1202	29.05	0.8933	0.1192	33.23	0.9466	0.1184	33.60	0.9520	0.0264
	30k	28.24	0.8820	0.1199	28.73	0.8877	0.1190	33.41	0.9466	0.1182	33.67	0.9524	0.0264
10	5k	33.64	0.9387	0.1251	33.64	0.9391	0.1244	37.87	0.9699	0.1182	38.85	0.9747	0.0275
	15k	34.12	0.9425	0.1211	34.17	0.9431	0.1187	38.40	0.9710	0.1190	39.37	0.9755	0.0259

TABLE I: Quantitative results of X-ray novel view synthesis on the X3D dataset under different numbers of training views.

Fig. 2: Visualization of results for the novel view synthesis task on X3D dataset.

View number	Method	None		+3DGS		+X-Gaussian		+ $\text{R}^{2}$ -Gaussian		+LINGO
View number	Method	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
5	FDK [ 15 ]	12.63	0.1183	20.05	0.2600	20.11	0.2621	22.98	0.3986	23.29	0.4139
	SART [ 1 ]	23.89	0.6614	21.38	0.5602	21.35	0.5633	24.61	0.7025	24.94	0.7202
	ASD-POCS [ 39 ]	23.38	0.6486	22.05	0.6113	22.18	0.6194	25.46	0.7488	25.78	0.7643
10	FDK [ 15 ]	16.13	0.1745	21.94	0.3075	21.98	0.3101	24.12	0.4153	24.37	0.4246
	SART [ 1 ]	26.22	0.7163	24.53	0.6480	24.55	0.6536	27.28	0.7614	27.76	0.7798

TABLE II: Quantitative results of CT reconstruction on the X3D dataset under different numbers of training views.

Fig. 3: Visualization of results for the CT reconstruction task on X3D dataset.

Fig. 4: Point cloud structures of different models under sparse-view conditions, along with 3D PSNR and 3D SSIM metrics.

Grad	Latent	Voxel	Init Time	Novel View Synthesis			CT Reconstruction
Scale	Init	Scale	Second $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	IPSD $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$
			1.42	46.09	0.9899	0.1129	32.61	0.8864
✓			1.42	46.77	0.9907	0.0906	32.78	0.8883
	✓		5.76	46.28	0.9899	0.0526	32.81	0.8911
✓	✓		5.76	46.74	0.9907	0.0321	32.75	0.8905
	✓	✓	0.47	46.49	0.9902	0.0472	32.67	0.8894

TABLE III: Impact of different modules on quantitative metrics under 25 views.

Sparse-View 3D Reconstruction

Sparse-view 3D reconstruction recovers scene geometry and appearance from a small number of images for novel-view rendering and 3D use.

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Sparse-view X-ray 3D reconstruction is essential for reducing radiation exposure, but recovering a density field from a handful of X-ray projections is severely ill-posed. Recently, 3D Gaussian Splatting has achieved state-of-the-art performance in sparse-view reconstruction by representing the volume using explicit, optimized primitives, but it requires dozens of projected views. With fewer views, reconstruction quality degrades severely since the explicit primitives are optimized freely without any anatomical information. Anatomical structures, in contrast, share similar geometry and density across a population. Their variations are bounded within a limited range that statistical shape models can capture. This paper proposes a shape-guided Gaussian splatting framework for sparse-view X-ray 3D reconstructions. Our contribution lies in driving Gaussian positions toward anatomically valid configurations, alongside atlas-based density regularization. Our method ensures anatomically consistent reconstruction and improves PSNR by 2.83 dB over a state-of-the-art Gaussian splatting baseline with as few as 5 views. Code Available: https://github.com/polyshape-lab/ShapeGuidedGaussian

Pranav Poudel, Florence Dell'Aniello Picard, Nairouz Shehata +2

Polytechnique Montréal, Canada · Mila - Quebec AI Institute, Canada · CHUM - University of Montreal Hospital, Canada

3D Gaussian Splatting 3D Medical Imaging Statistical Shape Modeling Sparse-View CT Reconstruction

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LUCID: Learned Undersampling-Adaptive Consistency-Guided Inference with Deterministic Flow Matching for Sparse-View CT Reconstruction

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.

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Sparse-View CT Reconstruction Computational Imaging Computed Tomography Image Inverse Problems

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CG-GLORE: A Conjugate Gradient-Based Global-Local Regularization Network for Sparse-View CT Reconstruction

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 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.

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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 +2

Sparse-View CT Reconstruction Computed Tomography Deep Unfolding

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Abstract

Sparse-View 3D Reconstruction

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