X-GRM: Large Gaussian Reconstruction Model for Sparse-view X-rays to Computed Tomography

## Abstract

Abstract Computed Tomography serves as an indispensable tool in clinical workflows, providing non-invasive visualization of internal anatomical structures. Existing CT reconstruction works are limited to small-capacity model architecture and inflexible volume representation. In this work, we present X-GRM (X-ray Gaussian Reconstruction Model), a large feedforward model for reconstructing 3D CT volumes from sparse-view 2D X-ray projections. X-GRM employs a scalable transformer-based architecture to encode sparse-view X-ray inputs, where tokens from different views are integrated efficiently. Then, these tokens are decoded into a novel volume representation, named Voxel-based Gaussian Splatting (VoxGS), which enables efficient CT volume extraction and differentiable X-ray rendering. This combination of a high-capacity model and flexible volume representation, empowers our model to produce high-quality reconstructions from various testing inputs, including in-domain and out-domain X-ray projections. Our codes are available at: https://github.com/CUHK-AIM-Group/X-GRM .

## 1 Introduction

Computed Tomography (CT) serves as an indispensable tool in disease diagnosis, treatment planning, and intraoperative guidance x_ray_1; x_ray_3; x_ray_4. Traditional reconstruction methods fdk; analytical_2; asd_pocs; sart typically require several hundred X-ray projections to achieve diagnostically acceptable image quality, exposing patients to excessive radiation and also consuming substantial resources. To address these limitations, our work investigates reconstructing CT volumes from sparse-view X-ray projections.

Existing sparse-view CT reconstruction approaches can be categorized into optimization-based and regression-based methods. Optimization-based methods iteratively refine 3D volumes to match X-ray projections using neural representations zha2022naf; shen2022nerp; zha2024r; cai2024radiative; sax_nerf or diffusion models chung2023solving; chung2023decomposed; lee2023improving. While effective, these approaches typically require minutes to even hours for reconstructing per case, making them impractical for time-sensitive applications. Regression-based methods fbpconvnet leverage neural networks to learn useful patterns for diverse reconstruction tasks-ranging from projection extrapolation anirudh2018lose; ghani2018deep and slice denoising wang2022dudotrans; jin2017deep; freeseed to direct volume regression difnet; dif_gs; c2rv. Despite enabling rapid inference, these approaches still face significant challenges: (1) they primarily employ small model architectures, like convolutional neural networks (CNNs), suffering from inherent scaling limitations, and (2) they primarily represent CT volumes as 3D voxels, which do not support differentiable X-ray rendering for incorporating X-ray constraints and render-related applications.

Very recently, X-LRM zhang2025x firstly proposes to use scalable transformer architectures trained on extensive datasets, while DeepSparse lin2025deepsparse similarly explores large-scale models for CT reconstruction. Both approaches achieve impressive reconstruction quality with computational efficiency. However, these methods rely on modified neural radiance fields zhang2025x or discrete 3D voxel representations lin2025deepsparse, which lack support for differentiable X-ray rendering—limiting their ability to incorporate direct X-ray constraints and rendering-based applications.

Figure: Figure 1: Our method achieves state-of-the-art reconstruction quality while maintaining the fastest runtime. (a) Qualitative results: DIF-Gaussian dif_gs exhibits issues with over-smooth results (red boxes) and R^2-Gaussian r2_gaussian has noise artifacts (orange boxes) and is time-consuming. In contrast, our method achieves better fidelity in a much shorter time. (b) Performance and runtime comparison: metrics are evaluated on the test set of collected large-scale dataset.
Refer to caption: extracted/6480364/Figures/introduction.png

To tackle these limitations, we propose a large feedforward X-ray Gaussian Reconstruction Model (X-GRM), for CT reconstruction from sparse-view X-ray projections. Our innovation is that a transformer-based architecture transformer, when coupled with flexible volume representations, can excel at CT reconstruction. Specifically, we develop a scalable X-ray Reconstruction Transformer that employs an encoder ViT to efficiently tokenize each X-ray projection in parallel, followed by a fusion ViT that integrates global information by performing self-attention across views. Secondly, inspired by the efficient rendering of 3D Gaussian Splatting kerbl20233d, we introduce a new volume representation, named Voxel-based Gaussian Splatting (VoxGS), where isometric 3D Gaussians are placed at voxel centers and rendering-related attributes are regressed from tokens. Such design enables efficient CT volume extraction and differentiable X-ray rendering, thereby introducing more constraints from X-ray inputs during training and also supports downstream render-related applications.
As shown in Fig. [1](https://arxiv.org/html/2505.15235v2#S1.F1), with the proposed scalable architecture and flexible volume representation, X-GRM drastically outperforms the SOTA methods in terms of both the reconstruction quality and inference speed.

In summary, the main contributions of our work are as follows:

- •
We introduce X-GRM, a large feed-forward Transformer model that, given sparse X-ray projection inputs, can directly predict the CT volume within one second.
- •
We introduce a flexible volume representation-Voxel-based Gaussian Splatting, which allows for efficient CT volume extraction and differentiable X-ray rendering.
- •
We demonstrate that X-GRM drastically outperforms existing methods in both the reconstruction quality and inference speed. Our codes and pre-trained models will be available.

## 2 Related work

### 2.1 Sparse-view CT reconstruction

Sparse-view CT reconstruction tackles the complex task of creating complete 3D volumetric data from a limited number of X-ray projections. Traditional methods sart; sauer1993local; sidky2008image frame this as maximum a posteriori estimation with statistical priors, but often produce poor quality reconstructions when very few views are available. Recent advances have employed neural radiance fields zha2022naf; shen2022nerp; sax_nerf or 3D Gaussian primitives cai2024radiative; ddgs; dgr; zha2024r as volume representations, which are gradually refined until their rendered X-rays match the input projections. Other approaches explore diffusion models as priors chung2023solving; chung2023decomposed; lee2023improving. While these methods deliver better results than traditional algorithms, they require extensive optimization time for each case, making them impractical for urgent clinical needs.

Feed-forward models offer a promising solution by directly mapping sparse projections to complete volumes with much faster inference times. These approaches include sinogram enhancement anirudh2018lose; ghani2018deep, cross-sectional image denoising wang2022dudotrans; jin2017deep; freeseed, and direct volume synthesis difnet; dif_gs; c2rv. Though significantly faster, these methods are limited by their architectural design and rigid volume representations. Recent works like X-LRM zhang2025x and DeepSparse lin2025deepsparse explore large foundation models for reconstruction, while our approach stands out through innovative architecture and 3D Gaussian volume representation—enabling both efficient reconstruction and high-quality X-ray rendering from any viewpoint, a capability missing in other approaches.

### 2.2 Feed-forward 3D object/scene reconstruction

Feed-forward reconstruction approaches aim to recover various 3D representations (e.g., mesh wang2018pixel2mesh; wu2020pq, implicit fields yu2021pixelnerf, 3DGS xu2024grm; charatan2024pixelsplat; chen2024mvsplat, and point maps wang2024dust3r) through a single forward pass from input images. Specifically, in the domain of feed-forward object generation, LRM hong2023lrm and its variants li2023instant3d; tochilkin2024triposr; wang2023pf; wei2024meshlrm; zhang2024gs; he2024lucidfusion; cai2024baking have achieved significant advances in both performance and efficiency by leveraging large-scale datasets deitke2023objaverse; deitke2023objaversexl and transformer architectures vaswani2017attention. Similarly, in feed-forward scene reconstruction, DUSt3R wang2024dust3r, pixelSplat charatan2024pixelsplat and subsequent variations mast3r; fast3r; mvdust3r; flare; cut3r; vggt; chen2024mvsplat; noposplat; wang2024freesplat; tang2024hisplat have produced impressive results through continuous scaling up of their approaches. However, CT reconstruction remains in its infancy, lacking sufficient generalization capabilities due to the use of small-scale model architectures and inflexible volume representations. In this work, we aim to tackle these limitations.

## 3 Method

### 3.1 Preliminaries

CT imaging forms the basis of computed tomography systems. When X-rays travel from source to detector, a projection ${\bm{I}}\in\mathbb{R}^{H\times W}$ captures the attenuation patterns through materials. For any ray ${\bm{r}}(t)={\bm{o}}+t{\bm{d}}\in\mathbb{R}^{3}$ with source intensity $I_{0}$ traversing from distance $t_{n}$ to $t_{f}$, the detected intensity $I^{\prime}({\bm{r}})$ adheres to the Beer-Lambert principle: $I^{\prime}({\bm{r}})=I_{0}\exp(-\int_{t_{n}}^{t_{f}}\sigma({\bm{r}}(t))dt)$, with $\sigma({\bm{x}})$ denoting the volumetric density at position ${\bm{x}}\in\mathbb{R}^{3}$. For numerical stability and analytical convenience, raw measurements undergo logarithmic transformation: $I(r)=\log I_{0}-\log I^{\prime}({\bm{r}})=\int_{t_{n}}^{t_{f}}\sigma({\bm{r}}(
t))dt$. This converts each measurement into a line integral of material density along the ray trajectory. The fundamental challenge in CT reconstruction involves recovering the underlying 3D density field $\sigma({\bm{x}})$ from a series of projections $\{{\bm{I}}_{i}\}_{i=1}^{K}$ acquired across $K$ distinct angular positions.

3D Gaussian Splatting kerbl20233d represents an approach to 3D content modeling through a collection of $N_{p}$ colored Gaussian primitives $\mathcal{G}=\{{\bm{g}}_{i}\}_{i=1}^{N_{p}}$. Each Gaussian element ${\bm{g}}_{i}=\exp\left(-\frac{1}{2}({\bm{x}}-\bm{\mu}_{i})^{\top}\bm{\Sigma}_{
i}^{-1}({\bm{x}}-\bm{\mu}_{i})\right)$ is characterized by its opacity $\bm{\sigma}_{i}\in\mathbb{R}$ and color ${\bm{c}}_{i}\in\mathbb{R}^{3}$ properties, alongside positional parameters $\bm{\mu}_{i}\in\mathbb{R}^{3}$ and covariance matrix $\bm{\Sigma}_{i}\in\mathbb{R}^{3\times 3}$ that encodes scaling ${\bm{s}}_{i}\in\mathbb{R}^{3}$ and orientation quaternion ${\bm{r}}_{i}\in\mathbb{R}^{4}$ within 3D space. This comprehensive set of attributes forms ${\bm{G}}\in\mathbb{R}^{N_{p}\times 14}$, capable of encoding complex 3D scenes or objects. By aligning the formula, the rasterization process is equivalent to the CT imaging procedure, thus we can use 3DGS to represent CT volumes and render X-rays (see Sec. [A.1](https://arxiv.org/html/2505.15235v2#A1.SS1) for more details). Our approach also modify the original 3DGS to address the distinct requirements of feed-forward CT reconstruction tasks.

### 3.2 Overview

Given a set of sparse-view X-ray projections $\mathcal{I}=\{{\bm{I}}_{i}\}_{i=1}^{K},({\bm{I}}_{i}\in\mathbb{R}^{H\times W})$ and their corresponding projection matrix $\mathcal{P}=\{{\bm{P}}_{i}\}_{i=1}^{K},{\bm{P}}_{i}={\bm{K}}_{i}[{\bm{R}}_{i}|
{\bm{t}}_{i}]$, calculated from via intrinsics matrix ${\bm{K}}_{i}$, rotation matrix ${\bm{R}}_{i}$, and translation vector ${\bm{t}}_{i}$, our goal is to learn a mapping $f_{\bm{\theta}}$ from X-ray projections to CT volume density field ${\bm{V}}\in\mathbb{R}^{M\times N\times L}$:

$$ $f_{\bm{\theta}}:\{{\bm{I}}_{i},{\bm{P}}_{i}\}_{i=1}^{K}\mapsto\{{\bm{V}}(x,y,z )|x\in[1,M],y\in[1,N],z\in[1,L]\},$ (1) $$

where we formulate $f_{\bm{\theta}}$ as a feedforward transformer and $\bm{\theta}$ are learnable parameters optimized from a large-scale training dataset. As illustrated in Fig. [2](https://arxiv.org/html/2505.15235v2#S3.F2), our method consists of a large X-ray Reconstruction Transformer to enhance the model scalability and a flexible voxel-based Gaussian Splatting that enables efficient CT volume extraction and differentiable rendering. In this section, we first describe the process of encoding X-ray inputs into compact latent tokens, integrated with camera information (Sec. [3.3](https://arxiv.org/html/2505.15235v2#S3.SS3)). Then, we discuss the design of VoxGS and how to regress Gaussian attributes from encoded tokens (Sec. [3.4](https://arxiv.org/html/2505.15235v2#S3.SS4)). Finally, we describe the model training details (Sec. [3.5](https://arxiv.org/html/2505.15235v2#S3.SS5)).

Figure: Figure 2: X-GRM is a large feed-forward transformer trained on a curated large CT reconstruction dataset. (a) X-ray Reconstruction Transformer efficiently encodes and fuses tokens from multiple X-ray projections, and (b) Voxel-based Gaussian Splatting enables both the efficient CT volume extraction and differentiable X-ray rendering.
Refer to caption: extracted/6480364/Figures/framework.png

### 3.3 X-ray Reconstruction Transformer

Existing CNN-based CT reconstruction methods difnet; dif_gs; c2rv face inherent scaling limitations that restrict their effectiveness for complex volumetric reconstruction. To overcome these constraints, we propose a large X-ray Reconstruction Transformer that significantly enhances CT reconstruction capabilities. Our approach employs an encoder ViT to efficiently tokenize X-ray projections in parallel, followed by a fusion ViT that integrates tokens across multiple views to reconstruct high-quality 3D volumes. Additionally, we incorporate camera geometry information into tokens through ModLN peebles2023scalable, enabling more precise spatial reasoning.

#### Encoder ViT.

We encode each X-ray projection ${\bm{I}}_{i}\in\mathcal{I}$ to a set of patch features ${\bm{H}}_{i}$, using a feature extractor $\mathcal{F}_{enc}$. This is done independently per image, yielding a sequence of image patch features ${\bm{H}}_{i}=\{h_{i,j}\}_{i,j=1}^{HW/P^{2}}$ for each image:

$$ ${\bm{H}}_{i}=\mathcal{F}_{enc}({\bm{I}}_{i}),i=1,...,K.$ (2) $$

Here we adopt transformer-based DINO zhang2022dino as our encoder. Before passing image features $\{{\bm{H}}_{i}\}_{i=1}^{K}$ to the decoder, we also inject Plücker ray directions into the features via adaptive layer norm peebles2023scalable:

$$ $\tilde{{\bm{H}}_{i}}=ModLN({\bm{H}}_{i},{\bm{R}}_{i}),i=1,...,K,$ (3) $$

where ${\bm{R}}_{i}$ is the Plücker ray embedding of the camera angle and origin. Unlike previous works that modulate camera poses to image features using extrinsic and intrinsic matrices hong2023lrm; liu2023zero, Plücker rays are defined by the cross product between the camera location and ray direction, offering a unique ray parameterization independent of scale, camera position and focal length.

#### Fusion ViT.

Most of the computation in our framework happens in the fusion ViT. We use a 16-layer transformer similar to ViT-B transformer. This fusion transformer takes
the concatenated encoded image patches from all views $\{\tilde{{\bm{H}}_{i}}\}_{i=1}^{K}$ and performs all-to-all self-attention $\mathcal{F}_{fuse}$:

$$ $\{{\bm{F}}_{1},{\bm{F}}_{2},...,{\bm{F}}_{K}\}=\mathcal{F}_{fuse}(\tilde{{\bm{ H}}_{1}},\tilde{{\bm{H}}_{2}},...,\tilde{{\bm{H}}}_{K}),$ (4) $$

where ${\bm{F}}_{i}$ is the fused token of $i$-th view. This operation provides features of each view with full context from all other views, enables complete spatial and context reasoning.

### 3.4 Voxel-based Gaussian Splatting

Existing feedforward models dif_gs typically represent CT as 3D voxels, yet it has limitations of supporting differentiable real-time rendering, thus can hardly leverage the X-ray projection constraints during the training period. Benefiting from highly optimized rasterization, 3DGS kerbl20233d enables real-time differentiable rendering. However, directly representing CT with original 3DGS or modified 3DGS for CT r2_gaussian; ddgs leads to inaccurate volume extraction and instable optimization for feedforward framework (Tab. [6(c)](https://arxiv.org/html/2505.15235v2#S4.T6.st3)). Therefore, we propose a new CT representation-Voxel-based Gaussian Splatting (VoxGS) to support precise volume extraction and differentiable X-ray rendering.

#### Voxel-based Gaussian Splatting.

VoxGS has two different designs with the original 3DGS. Firstly, it consists of 3D Gaussians $\mathcal{G}=\{{\bm{g}}_{i}\}_{i=1}^{N_{p}}$ with fixed positions. In particular, the position $\bm{\mu}_{i}$ of each Gaussian ${\bm{g}}_{i}$ is fixed at the centroid of each voxel grid ${\bm{V}}(x,y,z)$:

$$ $\bm{\mu}_{i}=(x,y,z),x\in[1,M],y\in[1,N],z\in[1,L].$ (5) $$

This design offers the advantage that when extracting CT volumes from 3D Gaussians $\mathcal{G}$, complex trilinear interpolation strategies are not required for identifying the voxel value, instead we can directly obtain it from the Gaussians opacities, which improves extraction speed and enables more stable optimization. Secondly, we remove the SH coefficients ${\bm{c}}_{i}$ related to color rendering from the Gaussian attributes, retaining only the opacity $\alpha_{i}$, the scale vector ${\bm{s}}_{i}$, and the rotation vector ${\bm{r}}_{i}$. This design is similar to r2_gaussian, where the kernel formulation removes view-dependent color because X-ray attenuation depends only on isotropic density. In summary, we can represent a CT volume as a set of voxel-based Gaussians: $\mathcal{G}=\{{\bm{g}}_{i}|{\bm{g}}_{i}=\{\bm{\mu}_{i},\alpha_{i},{\bm{s}}_{i}
,{\bm{r}}_{i}\},\bm{\mu}_{i}\text{ is fixed}\}_{i=1}^{N_{p}}$, from which X-ray projections can be efficiently rendered in a differentiable manner.

#### Decoding VoxGS attributes.

As Gaussian positions $\bm{\mu}_{i}$ is fixed, we only need to decode Gaussians attributes $\alpha_{i}$ and $\bm{\Sigma}_{i}$ from available view features $\{{\bm{F}}_{1},{\bm{F}}_{2},...,{\bm{F}}_{K}\}\subset\mathbb{R}^{H\times W
\times C}$, where $K$ is the number of X-ray projections. Specifically, for a 3D Gaussian ${\bm{g}}_{i}$ with fixed position $\bm{\mu}_{i}$, we query view-specific features $\tilde{{\bm{F}}}_{k}$ from ${\bm{F}}_{k}$:

$$ ${\bm{F}}_{k}^{i}=Interp({\bm{F}}_{k},{\bm{P}}_{k}(\bm{\mu}_{i}))\in\mathbb{R}^ {C},\text{ for }k=1,2,...,K,$ (6) $$

where ${\bm{P}}_{k}:\mathbb{R}^{3}\rightarrow{\mathbb{R}^{2}}$ is the projection matrix of $k$-th view, and $Interp(\cdot)$ denotes bilinear interpolation. Then, $K$ queried features are aggregated by a MaxPooling layer to obtain ${\bm{F}}^{i}_{max}=MaxPool({\bm{F}}_{1}^{i},{\bm{F}}_{2}^{i},...,{\bm{F}}_{K}^
{i})\in\mathbb{R}^{C}$. Finally, ${\bm{F}}^{i}_{max}$ is passed to several MLP layers to predict Gaussian parameters:

$$ $[\alpha_{i},{\bm{s}}_{i},{\bm{r}}_{i}]=MLPs({\bm{F}}_{max}^{i})\in\mathbb{R}^{ 1+3+4}.$ (7) $$

#### Volume extraction and X-ray rendering.

To extract the CT density volume ${\bm{V}}\in\mathbb{R}^{M\times N\times L}$, we can directly index the corresponding fixed Gaussian opacities $\alpha_{i}$:

$$ ${\bm{V}}(x,y,z)=\alpha_{i},\text{ where }\bm{\mu_{i}}=(x,y,z)^{T}.$ (8) $$

Benefiting from the fixed position design of VoxGS, extracting the density field can be achieved through fast indexing operations, without need of extra computation. While for X-ray rendering, we employ the rasterizer implemented in r2_gaussian to render projections in a differentiable manner, which enables more constraints from inputs X-rays and also support various downstream applications, like novel view synthesis and potential CT/X-ray registration.

### 3.5 Training objectives and protocols

#### Training objectives.

We train the network with two objectives: 1) to impose constraints on the predicted CT volume ${\bm{V}}$ such that it aligns with the ground truth ${\bm{V}}_{gt}$ and 2) to minimize the difference
between the actual X-ray projections ${\bm{I}}_{gt}$ and rendered ones ${\bm{I}}$. Accordingly, we adopt
two categories of losses: volume constraints and rendering constraints: $\mathcal{L}=\mathcal{L}_{volume}+\mathcal{L}_{render}$. Specifically, for volume reconstruction constraint $\mathcal{L}_{volume}$, we adopt MSE to compute point-wise estimation error:

$$ $\mathcal{L}_{volume}({\bm{V}},{\bm{V}}_{gt})=\sum_{x,y,z}({\bm{V}}(x,y,z)-{\bm {V}}_{gt}(x,y,z))^{2}.$ (9) $$

While for rendering constraint $\mathcal{L}_{render}$, we use a weight combination of photometric L1 loss $\mathcal{L}_{1}$ and D-SSIM loss $\mathcal{L}_{ssim}$ ssim:

$$ $\mathcal{L}_{render}({\bm{I}},{\bm{I}}_{gt})=\lambda_{L1}\mathcal{L}_{1}({\bm{ I}},{\bm{I}}_{gt})+\lambda_{ssim}\mathcal{L}_{ssim}({\bm{I}},{\bm{I}}_{gt}).$ (10) $$

#### Training protocols.

During the training period, we observe rendering with the original volume resolution $M\times N\times K$ ($256^{3}$ in this work), requires exhaustive GPU memory to preserve gradients. Therefore, we instead randomly sample sub-volumes $\tilde{{\bm{V}}}\in\mathbb{R}^{M/4\times N/4\times K/4}$ from the original volume ${\bm{V}}$, and modify the training objectives of Eq. [9](https://arxiv.org/html/2505.15235v2#S3.E9) accordingly. While during the inference, we directly use the full volume ${\bm{V}}$, as no gradients are required to store.

Figure: Table 1: The statistics of collected datasets.

## 4 Experiment

### 4.1 Experimental setup

#### Datasets.

To support the training of our scalable transformer with diverse anatomical data, we assemble an extensive dataset following X-LRM’s zhang2025x selection, combining 14,972 CT volumes and their corresponding X-ray projections from 8 public datasets (detailed in Tab.[1](https://arxiv.org/html/2505.15235v2#S3.T1)). This comprehensive repository spans the most clinically relevant body regions, including chest, abdomen, pelvis, and dental structures. For systematic model development and evaluation, we divided the collection into three distinct subsets: 13,612 volumes for training, 680 for validation, and 680 for testing. Complete specifications of these dataset partitions are thoroughly documented in Sec.[A.2](https://arxiv.org/html/2505.15235v2#A1.SS2).

For CT standardization, we meticulously normalize anatomical regions: chest, abdomen, and pelvic volumes are resampled to $50^{3}\text{cm}^{3}$ at $256^{3}$ voxel resolution, while dental acquisitions are calibrated to $40^{3}\text{cm}^{3}$ with the same resolution. We also transform radio-density measurements from native Hounsfield units (chest, abdomen, pelvis: [-1000, 1000]; dental: [-1000, 3000]) to a unified [0,1] scale, preserving crucial diagnostic information across key structures. To render X-ray projections from CT volumes in each dataset, we employ the TIGRE biguri2016tigre toolbox to generate synthetic radiographic projections—producing 50 high-definition views ($256^{2}$ resolution) distributed uniformly throughout the complete angular spectrum ($[0^{\circ},360^{\circ}]$). Clinical authenticity was enhanced through noise integration, combining Gaussian and Poisson distributions to accurately replicate quantum photon effects and Compton scatter phenomena.

#### Implementation details.

The proposed X-GRM is implemented with PyTorch pytorch and trained on 4 NVIDIA A100 (40G) GPUs. The model is optimized with AdamW loshchilov2017adamw for 100 epochs, with a batch size of 8 and $\beta_{1}=0.9,\beta_{2}=0.95$. The initial learning rate is set to $1\times 10^{-4}$ and gradually decreases to $1\times 10^{-6}$ following the cosine annealing scheduler loshchilov2016sgdr. For the model implementation, the encoder ViT $\mathcal{F}_{enc}$ uses a ViT-B/16 transformer architecture, initialized from DINO zhang2022dino pre-trained weights. The fusion ViT $\mathcal{F}_{fuse}$ is a ViT-B/16 model initialized from scratch, which has $16\times 16$ patch size, 12 layers, 12 heads, embedding dimension 768, and MLP ratio 4.0. We leverage
bFloat16 precision and gradient checkpointing to improve
GPU memory and computational efficiency.

During model training, we employ a variable-view learning strategy with the number of views randomly selected from ${6,8,10}$, with these perspectives evenly sampled from the 50 available projections. For quantitative evaluation, we utilize complementary metrics: PSNR calculated directly within the 3D volumetric space provides assessment of signal fidelity, while SSIM ssim averaged across multiple 2D slice comparisons offers insight into structural preservation, together providing a comprehensive measurement of reconstruction quality.

**Table 2: Quantitative comparison with traditional and feedforward methods. We evaluate all methods using the full test set (256^3 resolution) on one A100 GPU. All feedforward models are trained on the same training set. Bold: best results; underlined: second-best results.**
| Method | Time (s)$\downarrow$ | 6-View | 8-View | 10-View |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| PSNR$\uparrow$ | SSIM$\uparrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ |  |  |
| FDK fdk | 0.297 | 14.65 | 0.297 | 15.50 | 0.295 | 16.23 | 0.314 |
| ASD-POCS asd_pocs | 5.704 | 21.47 | 0.498 | 22.32 | 0.560 | 22.62 | 0.653 |
| SART sart | 21.091 | 21.89 | 0.634 | 22.52 | 0.642 | 23.66 | 0.685 |
| FBPConvNet fbpconvnet | 0.131 | 22.63 | 0.691 | 23.05 | 0.695 | 23.48 | 0.718 |
| FreeSeed freeseed | 0.508 | 24.67 | 0.781 | 24.89 | 0.789 | 25.43 | 0.790 |
| DIF-Net difnet | 1.561 | 22.27 | 0.684 | 22.72 | 0.688 | 23.27 | 0.714 |
| DIF-Gaussian dif_gs | 2.120 | 24.83 | 0.787 | 25.03 | 0.793 | 25.58 | 0.794 |
| X-GRM (Ours) | 0.928 | 28.39 | 0.873 | 28.86 | 0.879 | 29.21 | 0.886 |

Figure: Figure 3: Qualitative comparison with traditional and feedforward methods. Results shown are from the test set reconstructions with 10-view inputs.
Refer to caption: extracted/6480364/Figures/comparison1.png

### 4.2 Assessing CT reconstruction

Following the setup of X-LRM zhang2025x, we evaluate our X-GRM against existing CT reconstruction methods with two settings. Setting 1: evaluating on the full test set (680 samples) of the collected dataset. This setting includes traditional and feedforward methods, as they can efficiently handle massive X-ray inputs. To ensure fair comparison, we re-train the compared feedforward models on the same training set. Setting 2: evaluating on a sampled set (40 samples). This setting includes self-supervised approaches, as they typically require substantial optimization time. To cover diverse organs, we evenly sample five volumes from the test set of eight datasets.

Setting 1. We first compare with traditional methods (FDK fdk, SART sart, ASD-POCS asd_pocs) and feedforward methods (FBPConvNet fbpconvnet, FreeSeed freeseed, DIF-Net difnet, DIF-Gaussian dif_gs). As shown in Tab. [2](https://arxiv.org/html/2505.15235v2#S4.T2), X-GRM outperforms the compared models in both reconstruction quality and inference speed. When compared to FreeSeed, the SOTA 2D feedforward model, X-GRM achieves substantial improvements of 3.71dB, 3.97dB, and 3.78dB in PSNR for 6-view, 8-view, and 10-view inputs, respectively. Similarly, X-GRM outperforms DIF-Gaussian, the leading 3D feedforward method, by 3.56dB, 3.83dB, and 3.63dB while delivering $2\times$ inference speed. Some qualitative results are presented in Fig. [4](https://arxiv.org/html/2505.15235v2#S4.F4) (more results in Sec. [A.6](https://arxiv.org/html/2505.15235v2#A1.SS6)). Traditional methods like SART introduce prominent streak artifacts in sparse-view reconstructions. Meanwhile, feedforward approaches like FreeSeed and DIF-Gaussian suffer from significant blurring, particularly in bone structures and regions with low tissue contrast. In contrast, our proposed X-GRM method can preserve fine anatomical details while maintaining structural integrity.

Setting 2. We then compare with self-supervised methods (NAF zha2022naf, SAX-NeRF sax_nerf, R^2-Gaussian zha2022naf). As shown in Tab. [8](https://arxiv.org/html/2505.15235v2#A1.T8), X-GRM has clear advantages over existing self-supervised methods: it achieves the best reconstruction performance while requiring the least computational time. Compared to the second-fastest self-supervised method NAF, X-GRM is 200$\times$ faster, requiring only 0.9 second to reconstruct one CT volume of resolution 256^3. While compared to the state-of-the-art method SAX-NeRF and R^2-Gaussian, X-GRM delivers 4.78/4.34/3.85dB and 4.81/4.01/3.14dB higher PSNR when processing 6/8/10 inputs views. As evident from the reconstructed slices in Fig. [4](https://arxiv.org/html/2505.15235v2#S4.F4) (more results in Sec. [A.6](https://arxiv.org/html/2505.15235v2#A1.SS6)), NAF exhibit noise artifacts, SAX-NeRF produces less noise, but many anatomical structures are excessively smoothed, R^2-Gaussian better recovers anatomical structures, but exhibits many discontinuous regions, likely due to floating artifacts from 3DGS. In contrast, the reconstructed slices from X-GRM exhibit clearer anatomical structures, more accurate bone density, and fewer artifacts throughout the volume slices.

**Table 3: Quantitative comparison with self-supervised methods. We evaluate all methods using 40 CT volumes ($256^{3}$ resolution) sampled from the full test set on one RTX 4090Ti GPU. Bold and underlined values indicate best and second-best results.**
| Method | Time$\downarrow$ | 6-View | 8-View | 10-View |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| PSNR$\uparrow$ | SSIM$\uparrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ |  |  |
| NAF zha2022naf | 3.0m | 20.69 | 0.530 | 21.93 | 0.563 | 22.75 | 0.581 |
| SAX-NeRF sax_nerf | 48.5m | 22.93 | 0.686 | 23.82 | 0.702 | 24.62 | 0.730 |
| R^2-Gaussian r2_gaussian | 8.5m | 22.90 | 0.662 | 24.09 | 0.689 | 25.33 | 0.727 |
| X-GRM (Ours) | 0.9s | 27.71 | 0.838 | 28.16 | 0.846 | 28.47 | 0.854 |

Figure: Figure 4: Qualitative comparison with self-supervised models. Results shown are from the test set reconstructions with 10-view inputs.
Refer to caption: extracted/6480364/Figures/comparison2.png

Figure: Table 4: Cross-dataset reconstruction evaluation.

### 4.3 Assessing cross-dataset generalization

Due to the use of scalable architecture and large-scale training, X-GRM is inherently superior in generalizing to out-of-distribution inputs. To demonstrate this advantage, we conduct two cross-dataset evaluations. In particular, we use the models trained on the collected dataset, and directly test them on unseen PENGWIN liu2023pelvic (pelvis) and FUMPE masoudi2018 (chest) datasets. As evident in Tab. [4](https://arxiv.org/html/2505.15235v2#S4.T4), our X-GRM significantly outperforms other feedforward models, including FreeSeed, DIF-Net, and DIF-Gaussian. Compared to self-supervised models that uses per-sample optimization, our method also shows comparable or better performance, while delivering much faster inference speed (around 500× faster compared to R^2-Gaussian).

Figure: Table 5: Novel view synthesis results. Time: rendering time of one X-ray projection.
Refer to caption: extracted/6480364/Figures/nvs.png

### 4.4 Assessing novel X-ray synthesis

Novel X-ray synthesis enables clinicians to examine anatomical structures, enhancing diagnostic capabilities and also facilitating dataset augmentation. We evaluate X-GRM against established self-supervised methods that support X-ray synthesis using NeRF or 3DGS representations. Our evaluation is conducted on the test set comprising 30 distinct CT samples. For each sample, we use 10 projection views as input, and evaluate using the rest 40 unseen novel views. As reported in Tab.[5](https://arxiv.org/html/2505.15235v2#S4.T5), X-GRM delivers 12.55dB higher PSNR over R^2-Gaussian while maintaining fast rendering speeds of 0.02s for each projection. Qualitative analysis in Fig.[5](https://arxiv.org/html/2505.15235v2#S4.F5) shows that SAX-NeRF and R^2-Gaussian generate substantial noise artifacts at tissue-air interfaces (highlighted in red boxes), whereas X-GRM consistently preserves clear, well-defined anatomical boundaries.

### 4.5 Ablation study

Camera pose integration. We assess the effect of camera pose integration with two variants, ‘w/o pose’ that removes the pose integration, and ‘dense add’ that directly add the ray embeddings to the encoded tokens. As shown in Tab. [6(c)](https://arxiv.org/html/2505.15235v2#S4.T6.st3) (a), removing camera pose leads to 0.28db decline in PSNR, indicating pose information is necessary for reasoning CT geometry. Besides, ‘dense add’ delivers slightly worse results than ModLN, so we use ModLN as the final design.

Volume representation. We evaluate two alternative approaches: ‘w/o VoxGS’ that uses the voxel grid as the CT representation, and ‘VoxGS w/ shift’ that introduces a shift attribute to predict Gaussian positions, where CT volumes are extracted by querying from nearby 3D Gaussian distributions. As reported in Tab. [6(c)](https://arxiv.org/html/2505.15235v2#S4.T6.st3) (b), the ‘w/o VoxGS’ variant delivers 0.55dB lower PSNR, suggesting that the rendering constraints provided by the Gaussian representation benefit model learning. More importantly, the ‘VoxGS w/ shift’ variant delivers a performance drop of 2.37dB in PSNR. This likely stems from the inherent difficulty in optimizing precise Gaussian positions, and inaccuracies introduced during volume extraction.

Cross-view aggregation. We conduct ablation studies on cross-view aggregation strategies, evaluating ‘w/o attention’ which eliminates the fusion ViT component, and ‘cross-attention’ which substitutes self-attention in the fusion ViT with cross-attention mechanisms. As detailed in Tab. [6(c)](https://arxiv.org/html/2505.15235v2#S4.T6.st3) (c), removing attention results in a performance decline of 0.52dB in PSNR, confirming that effective cross-view information aggregation is essential for geometric reasoning. Meanwhile, the ‘cross-attention’ variant achieves comparable results to our self-attention implementation. Based on these findings, we adopt the self-attention approach for its implementation simplicity.

**Table 6: Ablation study of component designs on the ReconX-16K dataset with 10-view inputs.**
| Method | PSNR$\uparrow$ | SSIM$\uparrow$ |
| --- | --- | --- |
| w/o pose | 28.93 | 0.862 |
| dense add | 29.15 | 0.882 |
| Ours (ModLN) | 29.21 | 0.886 |

## 5 Conclusion

This paper presents X-GRM, a large feedforward model for reconstructing 3D CT volumes from sparse-view X-rays using a scalable transformer architecture and Voxel-based Gaussian Splatting representation. Trained on a large CT reconstruction dataset, X-GRM demonstrates superior reconstruction quality with sparse-view X-ray inputs. By addressing previous limitations in model capacity and volume representation, our work represents an advancement in non-invasive sparse-view CT imaging for clinical applications.

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## Appendix A Technical Appendices and Supplementary Material

### A.1 Represent CT volumes as 3D Gaussians

In 3D Gaussian Splatting (3DGS) methods [28] for natural scene rendering, the attenuation of light as it passes through a medium is described using an exponential transmittance model $T(t)$. This model is physically based on the Beer-Lambert law [56], representing the light propagation process from one point ${\bm{r}}(t_{0})$ to another point ${\bm{r}}(t)$ in space:

$$ $T(t)=\text{exp}(-\int_{t_{0}}^{t}\sigma({\bm{r}}(s))ds).$ (11) $$

Here, ${\bm{r}}(t)={\bm{o}}+t{\bm{d}}$ represents a 3D point along a ray with origin ${\bm{o}}$ and direction ${\bm{d}}$, while $\sigma({\bm{p}})$ denotes the density at point ${\bm{p}}$. As established in Sec. [3.1](https://arxiv.org/html/2505.15235v2#S3.SS1), X-ray attenuation follows an identical model. Consequently, 3DGS rendering can be directly leveraged for X-ray projection rasterization under a simplified imaging model that accounts solely for isotropic absorption (per Beer-Lambert law), with optional exclusion of color attributes.

### A.2 Dataset details

As stated in the main text, we follow X-LRM [77] to collect 8 public datasets covering organs and structures including chest, abdomen, pelvis, and teeth. We apply data standardization to adjust the data through three steps: resampling spacing, adjusting resolution to 256^3, clipping HU values, and normalizing to $[0,1]$. Then, we split each dataset into training/validation/test splits with ratio 20/1/1. Meanwhile, as most datasets solely contain CT volumes, we utilize the TIGRE toolbox [3] to render X-ray projections. The specific parameter settings for each dataset are shown in the Tab. [7](https://arxiv.org/html/2505.15235v2#A1.T7).

**Table 7: The parameters used to pre-process each subset of the collected dataset.**
| Dataset | # Volumes | Train/Val/Test | Spacing (mm) | Clipping range |
| --- | --- | --- | --- | --- |
| AbdomenAtlas v1.0 [32] | 5,171 | 4701/235/235 | [1.0,1.0,1.0] | [-1000, 1000] |
| RSNA2023 [20] | 4,711 | 4283/214/214 | [1.0,1.0,1.0] | [-1000, 1000] |
| LUNA16 [48] | 833 | 757/38/38 | [1.0,1.0,1.0] | [-1000, 1000] |
| AMOS [24] | 1,851 | 1683/84/84 | [1.0,1.0,1.0] | [-1000, 1000] |
| MELA [44] | 1,100 | 1000/50/50 | [1.0,1.0,1.0] | [-1000, 1000] |
| RibFrac [27, 69] | 660 | 600/30/30 | [1.0,1.0,1.0] | [-1000, 1000] |
| ToothFairy2 [4] | 223 | 203/10/10 | [0.3,0.3,0.3] | [-1000, 2000] |
| STSTooth [63] | 423 | 385/19/19 | [0.3,0.3,0.3] | [-1000, 2000] |

### A.3 Additional experiments of novel view synthesis

Due to space constraints, Tab. [5](https://arxiv.org/html/2505.15235v2#S4.T5) only presents results for novel view synthesis with 10 input views. Here, we further compare performance with 6 and 8 input views, as shown in the table. Our method consistently outperforms existing self-supervised approaches by a significant margin. In particular, compared to the current best method R^2-Gaussian, our approach delivers 14.92/13.01/11.18 dB improvement in performance with 6/8/10 input views, respectively. Meanwhile, our method achieves a rendering speed of 0.02s for each projection, meeting the requirements for most scenarios. We also provide more qualitative comparisons of these methods in Fig. [6](https://arxiv.org/html/2505.15235v2#A1.F6), from which we can observe that NAF fails to render correct structures, SAX-NeRF and R^2-Gaussian are prone to deliver artifacts. In contrast, our X-GRM can deliver obvious better rendering quality with more accurate bone density and clearer anatomical structures.

**Table 8: Additional experiments of novel view synthesis on the sampled test set (40 samples).**
| Method | Render Time (s)$\downarrow$ | 6-View | 8-View | 10-View |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| PSNR$\uparrow$ | SSIM$\uparrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ | PSNR$\uparrow$ | SSIM$\uparrow$ |  |  |
| NAF [76] | 0.448 | 23.11 | 0.404 | 26.07 | 0.463 | 28.29 | 0.505 |
| SAX-NeRF [6] | 0.916 | 27.72 | 0.562 | 29.09 | 0.603 | 31.85 | 0.659 |
| R^2-Gaussian [75] | 0.003 | 34.23 | 0.912 | 36.33 | 0.930 | 38.26 | 0.955 |
| X-GRM (Ours) | 0.020 | 49.15 | 0.991 | 49.34 | 0.992 | 49.44 | 0.993 |

Figure: Figure 6: Additional qualitative comparison of novel view synthesis.
Refer to caption: extracted/6480364/Figures/app_nvs.png

Figure: Figure 7: Qualitative comparison of reconstructed slices with traditional and feedforward models.
Refer to caption: extracted/6480364/Figures/app_s1.png

Figure: Figure 8: Qualitative comparison of reconstructed slices with self-supervised models.
Refer to caption: extracted/6480364/Figures/app_s2.png

### A.4 Limitations

X-GRM exhibits several limitations that remain future investigation. The model incurs increased memory consumption when utilizing excessive numbers of 3D Gaussians, and demonstrates suboptimal performance when reconstructing from extremely sparse inputs, particularly single X-ray projections. These challenges in future work through the implementation of efficient Gaussian pruning strategies and the integration of generative modeling approaches, which we leave as future works.

### A.5 Broader impacts

Impacts on real-world applications. X-GRM delivers superior reconstruction quality with faster inference speed, enabling efficient clinical deployment. Its accuracy and performance support time-sensitive diagnostic workflows while reducing patient radiation exposure. The VoxGS representation can potentially enable many downstream applications like CT/X-ray registration (as done in DDGS-CT [17]), extending the model’s utility beyond reconstruction to integrated clinical pipelines.

Impacts on research community. This work demonstrates the transformative potential of large-scale data and high-capacity models in medical imaging, encouraging similar approaches in related domains. By open-sourcing code, models, and data, X-GRM contributes essential resources for advancing medical image reconstruction research.

### A.6 More visualization

We provide more qualitative comparisons with traditional, feedforward, and self-supervised methods in Fig. [7](https://arxiv.org/html/2505.15235v2#A1.F7) and Fig. [8](https://arxiv.org/html/2505.15235v2#A1.F8). Our X-GRM consistently delivers better reconstruction quality with clearer anatomical structures and less noise artifacts.

## Peer Reviews

confidence: 5
contribution: 2
initial_rating: 2
presentation: 3
questions: See Weaknesses, please.
soundness: 2
strengths: - The paper addresses an important problem, real-time reconstruction for 3D CT imaging, with a clear and meaningful motivation.
- The proposed X-GRM is generally reasonable. Specifically, the ability of ViT to extract rich features from projection data has been well validated in prior works, and the 3D Gaussian Splatting framework indeed shows advantages in high-fidelity representation and real-time rendering. Thus, combining the two is technically sound.
- This work collects a large-scale dataset and conducts comprehensive experiments, which enhances the reliability of the proposed method.
- The paper is clearly written and easy to follow.
summary: This work proposes an X-ray Gaussian Reconstruction Method (X-GRM), a large supervised model for 3D sparse-view CT imaging. The proposed X-GRM consists of a scalable, pre-trainable ViT and VoxGS, a 3D Gaussian Splatting-based module. The ViT extracts features from input 2D projections, and VoxGS transforms these features into a 3D Gaussian Splatting representation. Finally, through voxelization and rendering, the model is optimized using losses defined in both the volume and projection domains. The proposed X-GRM is a feedforward model, enabling real-time 3D CT reconstruction. The experiments demonstrate its superiority over existing CT reconstruction methods (including both supervised and self-supervised ones) in terms of both running time and image quality.
weaknesses: - The motivation for using 3D GS to preserve high data fidelity is somewhat unclear. The paper claims to “support differentiable real-time rendering,” and thus employs 3D GS as a representation to incorporate X-ray physics. However, grid-based representations can also incorporate the X-ray forward model through ray-based rendering. Moreover, real-time rendering is not necessarily critical during model training. Please clarify this motivation.

- In line 232, the paper claims that “complex trilinear interpolation strategies are not required for identifying voxel values; instead, we can directly obtain them from Gaussian opacities.” However, in my opinion, trilinear interpolation is already quite simple. Please clarify what is meant here.

- The main difference between VoxGS and the original 3D GS is that VoxGS uses fixed Gaussian positions (i.e., means). In my opinion, this design choice is questionable. One major reason 3D GS performs well is its ability to adaptively adjust positions, scales, and shapes. Fixing the positions may significantly limit this adaptive capability.

- From the experimental results, although the proposed method outperforms the baselines, the reconstructed images still appear overly smooth and lack fine structural details, which may not meet the requirements of clinical diagnosis.

---

confidence: 5
contribution: 3
initial_rating: 4
presentation: 4
questions: - **On differentiable X-ray rendering and the motivation for VoxGS:**  
  The paper argues that recent methods such as X-LRM and DeepSparse cannot incorporate differentiable X-ray constraints. I have two related questions:  
  1. If a neural radiance field is used, why is differentiable X-ray rendering not supported? Additionally, with voxel-based representations and differentiable CT forward models (e.g., *torch-radon*, *TIGRE*, *DiffDRR*), such constraints should, in principle, be implementable.  
  2. According to the description, the 3D Gaussians in VoxGS are positioned on fixed voxel-grid coordinates, seemingly sacrificing adaptivity and spatial flexibility while incurring large memory costs. For instance, with a 256³ grid, does the model instantiate 256³ fixed-position Gaussians? How does this differ conceptually from a standard voxel representation? It seems the only potential gain lies in rasterization-based rendering speed—how significant is this improvement? The design appears to constrain the Gaussian representation to an extent that undermines its core advantages.  

- How long does the model take to train?  
- In Sec. 4.4 (X-ray synthesis), could the authors compare performance against self-supervised approaches on OOD datasets or under varying geometries?  
- Could additional qualitative visualizations be provided, especially for different anatomical regions (e.g., head)?
soundness: 3
strengths: - **Advanced architectural design.**  
  The paper effectively leverages recent advances in natural image modeling while addressing the unique challenges of CBCT reconstruction. The proposed *Scalable Cross-View Transformer Architecture* integrates a strong DiNO-based backbone for feature extraction and adopts *ModLN-conditioned Plücker rays* instead of simple attention-based camera embeddings. Adapting such advanced 3D vision techniques to medical CT reconstruction is a valuable contribution to the community.  

- **Clear writing and implementation details.**  
  The manuscript is clearly written, with detailed explanations of implementation procedures that substantially enhance reproducibility and transparency.
summary: The manuscript introduces X-GRM, a feed-forward transformer that reconstructs 3D CT volumes from sparse-view X-ray projections in a single pass. The method tokenizes each projection with an encoder ViT and fuses cross-view information with a multi-layer fusion ViT conditioned by Plücker ray embeddings. Decoding uses a new **Voxel-based Gaussian Splatting (VoxGS)** representation with fixed Gaussian centers at voxel locations, predicting opacity/scale/rotation to enable both fast volume extraction and differentiable X-ray rendering. Training jointly matches ground-truth volumes and rendered projections via MSE and weighted L1/SSIM losses. Experiments report higher PSNR/SSIM and faster runtime than traditional and feed-forward baselines, competitive advantages over self-supervised methods, cross-dataset generalization, and strong novel-view synthesis.
weaknesses: - **Missing key feed-forward baseline.**  
  Among feed-forward methods, the comparison omits the current SOTA approach **C²RV [1]**. The strongest baseline reported is DIF-Gaussian, which no longer represents the latest standard. I strongly recommend adding **C²RV** for a more complete comparison.  

- **Limited evaluation metrics.**  
  The paper evaluates reconstruction quality only with PSNR and SSIM. While X-GRM shows clear quantitative gains, qualitative results remain visually blurred. For ultra-sparse (6–10 view) CT scenarios, perfect reconstruction is unrealistic—these settings are often used for fast intra-operative localization. The authors are encouraged to include richer evaluation metrics such as downstream segmentation performance or key-organ volume estimation to better demonstrate practical utility.  

- **Insufficient qualitative analysis for cross-dataset generalization.**  
  Section 4.3 provides only quantitative metrics, without qualitative visualizations. Moreover, X-GRM’s numerical results appear comparable to DIF-Gaussian and R²-Gaussian, which does not convincingly demonstrate superior generalization.  

- **Limited validation of generalization claims.**  
  The generalization analysis is restricted to two OOD datasets, with marginal performance improvement. To substantiate the generalization claim, it would be valuable to include results under different CT acquisition geometries.


## References  

> [1] Lin, Yiqun, et al. **"C²RV: Cross-Regional and Cross-View Learning for Sparse-View CBCT Reconstruction."** *CVPR*, 2024.

---

confidence: 4
contribution: 2
initial_rating: 2
presentation: 3
questions: Please refer to weakness section.
soundness: 2
strengths: 1. The writing of the paper is satisfactory.
2. The usage of Voxel-based Gaussian is interesting and supports fast rendering and inference.
summary: This paper introduces X-GRM, a feed-forward model for reconstructing 3D CT volumes from sparse-view 2D X-ray projections. It aims to address limitations of existing methods, such as the slow inference of optimization-based approaches and the model capacity or representation constraints of other feed-forward models. The method has two primary components: an X-ray Reconstruction Transformer for encoding and fusing image features from multiple views, and a volume representation termed Voxel-based Gaussian Splatting (VoxGS). In this representation, 3D Gaussian positions are fixed at voxel centers, and the network predicts other attributes like opacity, scale, and rotation. This design allows for CT volume extraction through direct indexing and supports differentiable X-ray rendering, which is used to apply a rendering constraint during training. The authors report that X-GRM, when trained on a large dataset, demonstrated improved reconstruction quality and faster inference times (under one second) compared to several traditional, feed-forward, and self-supervised methods on their test set.
weaknesses: 1. The biggest concern I have is about the evaluations of this paper. The paper claims it creates a large-scale dataset following another paper, X-LRM. As most training/inference data are the same across two papers when checking them, I notice the scores reported for the same baseline using same evaluation metric has large discrepancy. The scores reported for baselines in this paper is on average 3-4db (15-20%) lower than those reported in X-LRM. This raises my concern if baseline evaluations are fair in this paper.

2. For baselines included in this paper, it lacks similar baselines that focus on sparse-view CT reconstruction. Most baselines included in this paper are not directly applied to sparse-view task. Additional baselines focused on this specific task should be included.

3. The paper's findings are based exclusively on simulated data. A key potential benefit of this large-scale model is its ability to generalize to data from different real-world scanners, but this practical application remains unevaluated by the authors.

4. The paper's exclusive evaluation in ultra-sparse settings, using 10 views or fewer, limits its applicability to real-world clinical scenarios. As shown in fig3,4,6,7 of the paper, the reconstruction quality is poor and far way off from real-world usage. Consequently, the method's utility for actual diagnostic or surgical guidance remains unevaluated and unclear.

---

confidence: 3
contribution: 3
initial_rating: 4
presentation: 3
questions: Real-data generalization: Since all training X-rays are synthetically generated from CT volumes using TIGRE, could the authors provide any preliminary evidence (even qualitative) that the model can generalize to real clinical X-rays with realistic noise and device geometry? Would fine-tuning on a small set of real X-rays be feasible?

1. Role of differentiable rendering: The paper emphasizes that VoxGS enables differentiable X-ray rendering, but the experiments do not clearly show how this component contributes to training or performance. Could the authors include an ablation or visualization that quantifies the benefit of the rendering loss?

2. Architecture scaling and efficiency: How does performance and runtime scale with model size (e.g., ViT-B vs. ViT-L) and number of input views? Are there diminishing returns when adding more views or layers?

3. Cross-dataset transfer: The cross-dataset test on PENGWIN and FUMPE is a good start—could the authors comment on how domain gaps (e.g., anatomy, scanner protocols) affect reconstruction? Is domain adaptation necessary?

4. Clinical interpretability and safety: Have the authors analyzed failure cases or potential clinical artifacts (e.g., missing fine structures, false positives in dense tissues)? Some discussion on interpretability or uncertainty estimation would strengthen the paper’s practical relevance.
soundness: 3
strengths: 1. Introducing a feed-forward paradigm for CT reconstruction — The paper extends the recent trend of large reconstruction models (e.g., LRM, GRM) into the medical imaging domain, proposing a purely feed-forward architecture for sparse-view CT that avoids per-case optimization and makes a conceptual step toward scalable “foundation models” for tomographic reconstruction.

2. High efficiency with competitive quality — The proposed model achieves state-of-the-art reconstruction performance while drastically reducing inference time to around one second per 256³ CT volume, demonstrating strong potential for real-time or clinical use cases where traditional iterative or diffusion-based methods are prohibitively slow.

3. Clear and accessible presentation — The paper is well organized and clearly written, with intuitive figures and straightforward technical explanations. The method’s motivation, architecture, and experiments are easy to follow even for readers outside the immediate subfield of CT reconstruction.
summary: The paper presents X-GRM, a large feed-forward Transformer model designed for reconstructing 3D CT volumes from sparse-view 2D X-ray projections. The method introduces two key components: an X-ray Reconstruction Transformer, which employs a per-view ViT encoder and a multi-view fusion ViT conditioned on camera geometry through ModLN for global spatial reasoning, and a novel Voxel-based Gaussian Splatting (VoxGS) representation that places fixed 3D Gaussians at voxel centers to enable both efficient CT volume extraction and differentiable X-ray rendering. The model is trained on nearly 15,000 CT volumes from eight public datasets, leveraging a combination of voxel-wise MSE loss and differentiable rendering constraints. Extensive experiments demonstrate that X-GRM achieves state-of-the-art reconstruction quality, outperforming both traditional iterative and modern feed-forward or self-supervised methods (e.g., FBPConvNet, FreeSeed, DIF-Gaussian, R2-Gaussian, SAX-NeRF) by 3–5 dB PSNR on average, while reconstructing a full 256³ CT volume in less than one second. Furthermore, the approach exhibits strong cross-dataset generalization and supports high-fidelity novel-view X-ray synthesis, highlighting its potential for scalable, real-time, and physically grounded sparse-view CT reconstruction in clinical settings.
weaknesses: 1. Limited realism and generalization — All training X-rays are synthetically rendered from CT volumes using the TIGRE simulator. The absence of experiments on real clinical radiographs makes it unclear how well the model generalizes to real-world acquisition noise, scanner geometry variations, or patient-specific artifacts.

2. Shallow experimental analysis — Although the paper reports many quantitative results, the ablation study remains minimal. Only three components (ModLN, VoxGS, and attention) are tested, while other key factors such as model size, number of input views, and fusion depth are not analyzed, leaving some architectural choices insufficiently justified.