\useunder

\ul

X-LRM: X-ray Large Reconstruction Model for
Extremely Sparse-View Computed Tomography Recovery in One Second

Guofeng Zhang^1,∗, Ruyi Zha^2,∗, Hao He³, Yixun Liang³, Alan Yuille¹ Hongdong Li², Yuanhao Cai^1,†
¹ Johns Hopkins University, ² Australian National University, ³ HKUST

Abstract

Sparse-view 3D CT reconstruction aims to recover volumetric structures from a limited number of 2D X-ray projections. Existing feedforward methods are constrained by the limited capacity of CNN-based architectures and the scarcity of large-scale training datasets. In this paper, we propose an X-ray Large Reconstruction Model (X-LRM) for extremely sparse-view ( $<$ 10 views) CT reconstruction. X-LRM consists of two key components: X-former and X-triplane. Our X-former can handle an arbitrary number of input views using an MLP-based image tokenizer and a Transformer-based encoder. The output tokens are then upsampled into our X-triplane representation, which models the 3D radiodensity as an implicit neural field. To support the training of X-LRM, we introduce Torso-16K, a large-scale dataset comprising over 16K volume-projection pairs of various torso organs. Extensive experiments demonstrate that X-LRM outperforms the state-of-the-art method by 1.5 dB and achieves 27 $\times$ faster speed and better flexibility. Furthermore, the downstream evaluation of lung segmentation tasks also suggests the practical value of our approach. Our code, pre-trained models, and dataset will be released at https://github.com/caiyuanhao1998/X-LRM

^†^†footnotetext:

*

= Equal Contribution.

\dagger

= Corresponding Author

1 Introduction

Computed Tomography (CT) uses X-rays with strong penetrating power to reveal internal structures non-invasively. It is widely used in medical imaging for disease diagnosis, treatment planning, and surgical navigation [13, 14, 24, 25]. In particular, CT reconstruction aims to recover the 3D radiodensity of the object given 2D X-ray projections.

Traditional methods [18, 67, 54, 2] usually require hundreds or even thousands of X-ray projections to yield good reconstruction quality, which exposes significant harmful radiation to patients and radiographers. Recently, some self-supervised algorithms based on neural radiance field (NeRF) [8, 68] or 3D Gaussian splatting (3DGS) [6, 70] have been designed to reconstruct CT with 40 $\sim$ 50 projections. Yet, these methods usually require a long time ( $\sim$ 15 minutes) for each reconstruction and the radiation doses are still relatively high. In this work, we study the extremely sparse-view ( $<$ 10 views) CT reconstruction in a feedforward manner to achieve fast inference speed in one second.

Refer to caption — Figure 1: Our X-LRM outperforms previous state-of-the-art 3D feedforward methods in terms of quality and efficiency, including DIF-Net [34], DIF-Gaussian [35], and C²-RV [36]. Our collected CT dataset, Torso-16K, is over 18 $\times$ larger than previous benchmarks: LUNA16 [52], ToothFairy [12], and AAPM-Myo [43].

Some recent works [27, 36, 35, 34, 40] also try to explore this task. However, existing feedforward methods suffer from the following issues. (i) They rely on single-organ datasets containing fewer than 1,000 cases [52, 12, 43], which severely lack the diversity and scale required to develop robust and generalizable models. (ii) Previous feedforward methods are mainly based on convolutional neural networks (CNNs), which exhibit limitations in effectively capturing long-range dependencies and achieving optimal scalability in large-scale training. (iii) The number of the input projections of existing methods is fixed and cannot be adjusted due to the computational scheme of CNN, which lacks flexibility and limits the application in practice.

To cope with these problems, we design an X-ray Large Reconstruction Model (X-LRM), for extremely sparse-view ( $<$ 10 views) CT recovery. X-LRM consists of two parts: X-former and X-triplane. Firstly, X-former uses a multi-layer perception (MLP) based image tokenizer to split an arbitrary number of input images into patch tokens. Then X-former adopts a pure Transformer [17] encoder to compute the self-attention among these patch tokens. The output tokens of the X-former are then upsampled and reshaped into our X-triplane representation. The point feature of the X-triplane is fed into an MLP to learn an implicit neural field of the 3D volume radiodensity. To explore the potential of large-scale training, we collect a 3D CT reconstruction dataset, Torso-16K, containing $\sim$ 16K volume-projection pairs. With the proposed techniques and dataset, our X-LRM can significantly benefit from large-scale training to boost the reconstruction performance and flexibly handle different numbers of input X-ray projections.

In a nutshell, our contributions can be summarized as:

•

We propose a novel feedforward framework, X-LRM, for extremely sparse-view CT reconstruction.
•

We design a Transformer-based encoder, X-former, to flexibly encode an arbitrary number of input X-ray projections. Besides, we present a new 3D representation, X-triplane, to model the radiodensity in X-ray imaging.
•

We collect a large-scale dataset, Torso-16K, containing over 16K samples of 2D X-ray projections and 3D CT volumes. To the best of our knowledge, our Torso-16K is the largest CT reconstruction benchmark and is over 18 $\times$ larger than the existing largest dataset in the literature.
•

Our X-LRM drastically outperforms the SOTA method by 1.5 dB in PSNR and achieves $27\times$ faster inference speed.

2 Related Work

2.1 Sparse-View CT Reconstruction

We adopt a cone-beam CT (CBCT) setup that acquires multi-view 2D X-ray projections for volumetric reconstruction. Existing sparse-view CT reconstruction approaches can be categorized into optimization-based and prediction-based methods. Optimization-based methods iteratively refine the 3D volume to align with the measured projections. Traditional methods [2, 51, 55] formulate reconstruction as a maximum a posteriori problem, while learning-based methods leverage neural representations [68, 53, 7, 70, 6] and diffusion models [10, 11, 31]. Despite their effectiveness, these methods typically require minutes to hours to process a single case, making them impractical for real-time clinical applications. Prediction-based methods, in contrast, utilize neural networks such as CNNs [50] to learn semantic priors from external datasets. Given a test case, they employ pre-trained models for projection extrapolation [3, 19], slice denoising [59, 28, 40], or volume regression [34, 35, 36]. While these methods enable rapid inference, they are constrained by the limited capacity of CNN-based architectures and the scarcity of large-scale training datasets. We aim to cope with these problems with our X-LRM model.

2.2 Feedforward 3D Reconstruction

Unlike optimization-based methods NeRF [45] or 3D gaussian splatting [30], which take time-consuming optimization phase for shape recovery, feedforward 3D reconstruction aims to learn diverse geometry types (e.g., mesh [60, 64], implicit fields [44, 65] etc.) from input images in a forward manner with neural network architectures. Boosting from large-scale 3D datasets like Objaverse-XL [16, 15] and the scalability of Transformer architectures [58], Large Reconstruction Model [23] and its subsequent variants [32, 56, 61, 63, 71, 20, 9] has greatly promoted reconstruction ability and efficiency of current fields. However, due to the data scarcity of CT reconstruction and 3D model embedding, current feedforward CT reconstruction methods often suffer from poor reconstruction quality and generalization ability. Our goal is to fill these research gaps.

3 Method

The pipeline of our method is shown in Fig. 2. Our X-LRM consists of two parts: X-former and X-triplane, corresponding to Fig. 2 (b) and Fig. 2 (c). X-former begins with an MLP-based image tokenizer. Then a Transformer-based encoder processes an arbitrary number of multi-view image tokens with view-associated ray information into patch-based features. These features are then mapped into triplane tokens through cross-attention in a triplane decoder. We upsample and unpatchify these tokens to form our X-triplane representation. Finally, we adopt an MLP to learn an implicit mapping from the 3D point features on the triplane to the corresponding volume radiodensity.

3.1 X-former

As aforementioned, existing feedforward methods, primarily CNN-based, struggle with large-scale training, capturing long-range dependencies, and handling varying numbers of projections. These limitations lead to unsatisfactory performance and poor flexibility. To cope with these problems, we design an X-former consisting of an MLP-based image tokenizer and a Transformer-based image encoder.

Image Tokenizer. As shown in Fig. 2 (b), the input to the tokenizer is multi-view X-ray projections $\mathbf{I}_{i}\in\mathbb{R}^{H\times W\times 1}$ concatenated with the corresponding viewpoint camera conditions $\mathbf{C}_{i}\in\mathbb{R}^{H\times W\times 6}$ . We denote the input at the $i$ -th view as $\mathbf{X}_{i}=[\mathbf{I}_{i},\mathbf{C}_{i}]\in\mathbb{R}^{H\times W\times 7}$ . During training, X-former can take varying numbers of views, denoted as $\mathcal{V}=\{V_{1},V_{2},\dots,V_{m}\}$ , where $m$ is the count of varying numbers of input views. For a specific $V_{i}$ , the input is denoted as $\mathbf{X}=[\mathbf{X}_{1},\mathbf{X}_{2},\dots,\mathbf{X}_{V_{i}}]\in\mathbb{R}^{V_{i}\times H\times W\times 7}$ , where $V_{i}\in\mathbf{V}$ can change dynamically during training.

Specifically, we adopt the Reference-Point Plücker Coordinate (RPPC) [9] as our camera conditions since it provides more information of the ray position and the relative depth than standard Plücker Coordinate. Thus, we have $\mathbf{C}_{i}=\left(\mathbf{o}_{i}-(\mathbf{o}_{i}\cdot\mathbf{d}_{i})\mathbf{d}_{i},\mathbf{d}_{i}\right)$ , which better captures spatial relationships. Here, $\mathbf{o}_{i}$ and $\mathbf{d}_{i}$ represent the origins and directions of the pixel-aligned rays at the $i$ -th view.

Subsequently, the tokenizer partitions each input view into non-overlapping patches and projects each patch into a latent space of dimension $d_{E}$ via an MLP layer. Then we fuse patchified tokens of different views by concatenating them to derive the initial patch-wise tokens $\mathbf{H}\in\mathbb{R}^{n\times d_{E}}$ .

Image Encoder. The feature tokens ${\mathbf{H}}$ are then encoded by a Transformer-based image encoder to produce input feature tokens: $\mathbf{F}\in\mathbb{R}^{n\times d_{E}}$ , where $d_{E}$ is the hidden dimension of our image encoder. The image encoder consists of $N_{e}$ self-attention blocks [58], and each block comprises a multi-head self-attention layer and an MLP layer. We add layer normalization [4] before both layers. For the $j$ -th self-attention block, we first split input $\mathbf{H}^{j}_{in}$ into $k_{E}$ heads as

\mathbf{H}^{j}_{in}=[\mathbf{H}^{j}_{1},\mathbf{H}^{j}_{2},\dots,\mathbf{H}^{j}_{k_{E}}].

(1)

Then for the $i$ -th head, we project input $\mathbf{H}^{j}_{i}$ into query $\mathbf{Q}^{j}_{i}\in\mathbb{R}^{n\times d_{ke}}$ , key $\mathbf{K}_{i}^{j}\in\mathbb{R}^{n\times d_{ke}}$ , and value $\mathbf{V}_{i}^{j}\in\mathbb{R}^{n\times d_{ke}}$ as

\mathbf{Q}_{i}^{j}=\mathbf{H}_{i}^{j}\mathbf{W}_{\mathbf{Q}_{i}^{j}},\;\mathbf{K}_{i}^{j}=\mathbf{H}_{i}^{j}\mathbf{W}_{\mathbf{K}_{i}^{j}},\;\mathbf{V}_{i}^{j}=\mathbf{H}_{i}^{j}\mathbf{W}_{\mathbf{V}_{i}^{j}},

(2)

where $\mathbf{W}_{\mathbf{Q}_{i}^{j}}$ , $\mathbf{W}_{\mathbf{K}_{i}^{j}}$ , $\mathbf{W}_{\mathbf{V}_{i}^{j}}\in\mathbb{R}^{d_{E}\times d_{ke}}$ are learnable parameters of the $fc$ layers and $d_{ke}=d_{E}/k_{E}$ . Then the output of $i$ -th head of the $j$ -th self-attention layer $\mathbf{A}_{i}^{j}$ is computed as

{\mathbf{A}_{i}^{j}}=\text{softmax}\left(\frac{\mathbf{Q}_{i}^{j}(\mathbf{K}_{i}^{j})^{\top}}{\sqrt{d_{ke}}}\right)\mathbf{V}_{i}^{j}+\mathbf{H}_{i}^{j}.

(3)

Then $k_{E}$ heads are concatenated to pass through a fully connected ( $fc$ ) layer to derive the output of self-attention as

{\mathbf{H}^{j}_{mid}}=[\mathbf{A}_{1}^{j},\;\mathbf{A}_{2}^{j}\;\dots\;\mathbf{A}_{k_{E}}^{j}]\;\mathbf{W}^{j}_{s}.

(4)

where $\mathbf{W}^{j}_{s}\in\mathbb{R}^{d_{E}\times d_{E}}$ is the learnable parameter of the $fc$ layer. Then we forward $\mathbf{H}^{j}_{mid}$ to the MLP layer:

\mathbf{H}^{j}_{out}=\sigma(\mathbf{H}^{j}_{mid}\mathbf{W}_{1}+\mathbf{b}_{1})\mathbf{W}_{2}+\mathbf{b}_{2}+\mathbf{H}^{j}_{mid},

(5)

where $\sigma$ is the activation function, and $\mathbf{W}_{1},\mathbf{W}_{2},\mathbf{b}_{1},\mathbf{b}_{2}$ are learnable parameters of $fc$ layers. Finally, the output of the last layer of the image encoder is $\mathbf{F}=\mathbf{H}^{N_{e}}_{out}\in\mathbb{R}^{n\times d_{E}}$ . This aforementioned process is illustrated in Fig. 2 (b)

Our X-former leverages the inherent flexibility of the transformer architecture, which can naturally process input tokens of different lengths. This allows our model to seamlessly train with different numbers of input views within a single training session, boosting the reconstruction performance and resulting in a unified framework capable of handling diverse multi-view configurations.

Dataset	Body Parts	# of Volumes
AbdomenAtlas v1.0 [33]	Abdomen, Chest, Pelvis	5,171
RSNA2023 [21]	Abdomen, Pelvis	4,711
AMOS [26]	Abdomen	1,851
PENGWIN [37]	Pelvis	100
TCIA [1, 46]	Abdomen	833
MELA [47]	Chest	1,100
FLARE24 (subset) [41]	Abdomen, Chest	1,868
FUMPE [42]	Chest	35
LNDb [49]	Chest	294
RibFrac [29, 66]	Abdomen, Chest	660
Torso-16K (Ours)	Abdomen, Chest, Pelvis	16,623

3.2 X-triplane

To lift the features from 2D projection into 3D space, we design a Transformer-based decoder to map the 2D patch-wise features $\mathbf{F}$ into 3D triplane tokens $\mathbf{Z}\in\mathbb{R}^{(3\times 32\times 32)\times d_{D}}$ , where $d_{D}$ is the hidden dimension of the triplane decoder. $\mathbf{Z}$ is later upsampled and reshaped into our X-triplane representations. Then we adopt an MLP to learn an implicit mapping from the 3D point feature on the triplane representation to the corresponding radiodensity.

Triplane Decoder. As shown in Fig. 2 (c), the input of the triplane decoder includes $\mathbf{F}$ and a set of learnable triplane embeddings $\mathbf{E}\in\mathbb{R}^{(3\times 32\times 32)\times d_{D}}$ . Our triplane decoder has $N_{d}$ cross-attention blocks. Each cross-attention block comprises a cross-attention layer, a self-attention layer, and an MLP layer. To guide the reconstruction of the triplane tokens and lift the feature into 3D space, we adopt the cross-attention mechanism to extract 2D projection and camera information by querying the input feature $\mathbf{F}$ .

Similar to self-attention, for the $j$ -th cross-attention block in our triplane decoder, we first split $\mathbf{F}$ and input triplane embeddings $\mathbf{E}^{j}_{in}$ into $k_{D}$ heads as

	$\displaystyle\mathbf{F}$	$\displaystyle=[\mathbf{F}_{1},\mathbf{F}_{2},\dots,\mathbf{F}_{k_{D}}],$		(6)
	$\displaystyle\mathbf{E}^{j}_{in}$	$\displaystyle=[\mathbf{E}^{j}_{1},\mathbf{E}^{j}_{2},\dots,\mathbf{E}^{j}_{k_{D}}].$		(6)

Then for the $i$ -th cross-attention head, we project $\mathbf{F}_{i}$ into query $\mathbf{Q}_{i}^{j}\in\mathbb{R}^{n\times d_{kd}}$ , and project $\mathbf{E}_{i}^{j}$ into key $\mathbf{K}_{i}^{j}\in\mathbb{R}^{(3\times 32\times 32)\times d_{kd}}$ and value $\mathbf{V}_{i}^{j}\in\mathbb{R}^{(3\times 32\times 32)\times d_{kd}}$ by three $fc$ layers, where $d_{kd}=d_{D}/k_{D}$ . Then the output of $i$ -th head of the $j$ -th cross-attention layer $\mathbf{B}_{i}^{j}$ is computed as

{\mathbf{B}_{i}^{j}}=\text{softmax}\left(\frac{\mathbf{Q}_{i}^{j}(\mathbf{K}_{i}^{j})^{\top}}{\sqrt{d_{kd}}}\right)\mathbf{V}_{i}^{j}+\mathbf{E}_{i}^{j}.

(7)

Subsequently, $k_{D}$ heads are concatenated to pass through an $fc$ layer for the output of the cross-attention layer:

{\mathbf{E}_{mid}^{j}}=[\mathbf{B}_{1}^{j},\;\mathbf{B}_{2}^{j}\;\dots\;\mathbf{B}_{k_{D}}^{j}]\;\mathbf{W}^{j}_{c},

(8)

where $\mathbf{W}^{j}_{c}\in\mathbb{R}^{d_{D}\times d_{D}}$ is parameter of $fc$ layer. Similar to previous self-attention (SA) and MLP in Sec. 3.1 we have

\mathbf{E}^{j}_{out}=\text{MLP}\big{(}\text{SA}(\mathbf{E}^{j}_{mid})+\mathbf{E}^{j}_{mid}\big{)}+\text{SA}(\mathbf{E}^{j}_{mid}).

(9)

Finally, the output of the last layer of our triplane decoder is $\mathbf{Z}=\mathbf{E}^{N_{d}}_{out}\in\mathbb{R}^{(3\times 32\times 32)\times d_{D}}$ , as illustrated in Fig. 2 (c). $\mathbf{Z}$ is further upsampled by a deconvolution layer and unpatchified to our X-triplane representation T.

Type	Method	Time (s) $\downarrow$	6-View		8-View		10-View
Type	Method	Time (s) $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
Traditional	FDK	0.008	9.51	0.039	10.68	0.047	11.46	0.058
	ASD-POCS	1.385	22.17	0.573	23.40	0.612	24.62	0.667
	SART	1.400	22.61	0.537	23.56	0.548	24.57	0.585
2D Feedforward	FBPConvNet	\ul0.010	26.99	0.704	27.22	0.722	28.05	0.737
2D Feedforward	FreeSeed	0.163	28.93	0.841	\ul30.08	0.843	30.17	0.855
3D Feedforward	DIF-Net	0.445	26.10	0.627	26.81	0.663	27.47	0.708
	DIF-Gaussian	0.621	28.19	0.813	28.53	0.820	29.52	0.848
	C²RV	3.837	\ul29.51	\ul0.850	29.83	\ul0.849	\ul30.96	\ul0.871
	X-LRM (Ours)	0.141	31.05	0.910	31.24	0.912	31.33	0.915

Table 2: Comparison with traditional and feedforward methods on 750 test cases. Best result is in bold and second-best is \ulunderlined.

Triplane Implicit Neural Field. Our X-triplane $\mathbf{T}$ is composed of three orthogonal feature planes: $\mathbf{T}_{xy}$ , $\mathbf{T}_{yz}$ , and $\mathbf{T}_{xz}\in\mathbb{R}^{(64\times 64)\times d_{T}}$ , where $64\times 64$ refers to the spatial resolution of each plane and $d_{T}$ is the dimension of the point feature $\mathbf{P}_{\boldsymbol{x}}\in\mathbb{R}^{3\times d_{T}}$ . Then we build an implicit neural field mapping from the position of a 3D point to its radiodensity.

For a given 3D point $\boldsymbol{x}=(x,y,z)\in[-1,1]^{3}$ within the unit bounding box (where each coordinate is normalized), we obtain its feature embeddings by projecting it onto three orthogonal plane features $\mathbf{T}_{xy},\mathbf{T}_{yz},$ and $\mathbf{T}_{xz}$ at $\mathbf{p}_{xy}=(x,y),\mathbf{p}_{yz}=(y,z),$ and $\mathbf{p}_{xz}=(x,z)$ . We then apply bilinear interpolation to extract features from each plane. Take the $xy$ -plane $\mathbf{T}_{xy}$ and a point $\mathbf{p}_{xy}=(x,y)$ for instance, the interpolated feature value is computed as

$\displaystyle\mathbf{T}_{xy}(\mathbf{p}_{xy})$	$\displaystyle=(1-\alpha)\beta\mathbf{T}(x_{0},y_{1})$	(10)
	$\displaystyle+\alpha(1-\beta)\mathbf{T}_{xy}(x_{1},y_{0})$
	$\displaystyle+(1-\alpha)(1-\beta)\mathbf{T}_{xy}(x_{0},y_{0})$
	$\displaystyle+\alpha\beta\mathbf{T}_{xy}(x_{1},y_{1}),$

where $x_{0},x_{1}$ and $y_{0},y_{1}$ are the neighboring grid points, and the interpolation weights are $\alpha=x-x_{0}$ , $\beta=y-y_{0}$ . Applying this bilinear interpolation to all three triplanes, we obtain the feature representation at the point $\boldsymbol{x}$ as

\mathbf{P}_{\boldsymbol{x}}=\left(\mathbf{T}_{xy}(\mathbf{p}_{xy}),\mathbf{T}_{yz}(\mathbf{p}_{yz}),\mathbf{T}_{xz}(\mathbf{p}_{xz})\right).

(11)

As the radiodensity is isotropic and only related to the point property, we adopt an MLP to learn the mapping $f_{\text{INF}}$ from the point feature $\mathbf{P}_{\boldsymbol{x}}$ to the radiodensity $\rho_{\boldsymbol{x}}$ as

f_{\text{INF}}:\left(\mathbf{T}_{xy}(\mathbf{p}_{xy}),\mathbf{T}_{yz}(\mathbf{p}_{yz}),\mathbf{T}_{xz}(\mathbf{p}_{xz})\right)\rightarrow\rho_{\boldsymbol{x}}.

(12)

3.3 Training objective

Existing RGB 3D reconstruction methods mainly adopt 2D rendering training loss to achieve good image recovery quality. However, this supervision involves volume rendering that needs to sample many 3D points to compute for each ray, taking a long time. Besides, in X-ray imaging, the 3D CT reconstruction is more concerned than the 2D X-ray rendering. Thus, we adopt the more precise 3D reconstruction loss with varying numbers of input views as

\mathcal{L}_{recon}=\frac{1}{m}\sum_{V_{i}\in\mathcal{V}}\big{|}\big{|}~{}\hat{\mathbf{U}}_{V_{i}}-\mathbf{U}_{gt}\big{|}\big{|}^{2},

(13)

where $\mathcal{V}=\{V_{1},V_{2},\dots,V_{m}\}$ represents the training settings with different input view numbers $V_{i}$ , $\hat{\mathbf{U}}_{V_{i}}$ refers to the CT volume reconstructed by our X-LRM given $V_{i}$ numbers of input views, and $\mathbf{U}_{gt}$ is the ground-truth CT volume.

Type	Method	Time $\downarrow$	6-View		8-View		10-View
Type	Method	Time $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$	PSNR $\uparrow$	SSIM $\uparrow$
Self-Supervised	NAF	11m	23.86	0.644	24.64	0.654	25.38	0.685
	R²-Gaussian	\ul6m	20.28	0.528	20.79	0.529	22.09	0.581
	SAX-NeRF	8h	24.08	0.669	24.73	0.674	25.68	0.692
Diffusion Based	DDS	12m	24.42	0.529	25.64	0.570	26.64	0.607
Diffusion Based	DiffusionMBIR	11h	\ul26.61	\ul0.734	\ul28.51	\ul0.803	\ul30.05	\ul0.835
3D Feedforward	X-LRM (Ours)	0.14s	30.14	0.888	30.10	0.886	30.28	0.889

Table 3: Comparison with self-supervised and diffusion-based methods on 10 test cases. Our method is 3.53 dB higher and 2570

\times

faster.

4 Experiment

4.1 Experimental Setup

Datasets.

Previous works rely on small datasets [43, 12, 52] (fewer than 1,000 samples), which limits the ability to train robust and generalizable models. To overcome this constraint, we introduce Torso-16K, the largest and most diverse CT reconstruction dataset, comprising 16,623 real-world CT scans from ten public datasets (Fig. 3). It covers key anatomical regions in clinical applications, including the chest, abdomen, and pelvis. Some examples are shown in Fig. 3. Torso-16K is split into 15,000 / 873 / 750 for training, validation, and testing. We standardize CT scans by resampling and cropping them to a 50³ cm³ volume at 128³ resolution. Radiodensity values are normalized from the Hounsfield unit range [-1000, 1000] to [0,1], ensuring coverage of primary organs of interest. Since most public datasets only provide CT volumes, we render multi-view X-ray projections via the TIGRE toolbox [5]. These 256² resolution projections span a full range 0 ${}^{\circ}\sim$ 360^∘ with 3.9² mm² pixel spacing. To enhance realism, we add Gaussian and Poisson noise to simulate Compton scattering and adopt the UCT 960+ scanner [57], with a 0.6m source-object distance and 1.118m source-detector distance.

Implementation Details.

We implement X-LRM by PyTorch [48]. X-LRM is trained with the AdamW optimizer [39] ( $\beta_{1}=0.9$ , $\beta_{2}=0.95$ ). The weight decay coefficient $\lambda$ is set to 0.05. The initial learning rate is set to $4\times 10^{-4}$ and follows a cosine annealing scheduler [38] with a warm-up phase of $3000$ iterations. For the network architecture, we utilize a ViT-B/16 transformer encoder, which processes $256\times 256$ inputs to $257$ feature tokens at an embedding dimension of $d_{E}=384$ with $N_{e}=12$ layers. The transformer decoder consists of $N_{d}=12$ layers at an output dimension of $d_{D}=512$ , while the X-triplane has a feature dimension of $d_{T}=32$ . The MLP used for radiodensity queries has four layers with a hidden dimension of $64$ .

During training, our model is designed to learn from a set of possible input view counts, $V=\{6,8,10\}$ . For each epoch, the same instance is processed 3 times, each with a different number of views selected from $V$ . Training is conducted on 8 RTX A5000 GPUs at a per-gpu batch size of $6$ for $100$ epochs. For evaluation, we adopt the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) [62] as the quantitative metrics. Please note that PSNR is measured directly in 3D space and SSIM is computed as the average of 2D SSIM values.

Method	Recon.		Left Lung		Right Lung
Method	PSNR	SSIM	DICE	ASD $\downarrow$	DICE	ASD $\downarrow$
FDK	9.14	0.03	0.34	43.41	0.26	45.12
SART	21.7	0.51	28.29	13.44	2.92	28.12
ASD-POCS	21.48	0.53	25.35	15.62	2.52	31.84
FBPConvNet	26.02	0.68	\ul93.59	\ul0.65	\ul93.58	\ul0.56
FreeSeed	27.77	\ul0.83	91.01	1.07	90.56	0.82
DIF-Net	24.71	0.55	84.63	1.70	84.78	1.44
DIF-Gaussian	26.84	0.79	92.16	0.83	91.69	0.72
C²RV	\ul28.24	\ul0.83	91.47	0.88	90.28	0.87
X-LRM (Ours)	30.59	0.92	95.21	0.49	94.63	0.48

Table 4: Quantitative lung segmentation comparison of traditional and feedforward methods for 6-view reconstructed CTs.

4.2 Comparison with State-of-the-Art Methods

We evaluate our X-LRM model against baseline methods under different numbers of projection views (i.e. 6, 8, 10) using the following two different settings:

•

Traditional and feedforward methods: Traditional methods are directly tested on the 750-sample test set. The feedforward methods are first trained on the train set and then tested on the 750-sample test set.
•

Self-supervised and diffusion-based methods: We use a subset of 10 samples selected from the 750-sample test set, ensuring all 10 sub-datasets in Fig. 3 are covered. We test on this small dataset due to the long inference time (up to 11 hours per sample) of these methods.

Quantitative Results. Firstly, we compare X-LRM with three traditional methods (FDK [18], SART [2], and ASD-POCS [54]) and five feedforward methods (FBPConvNet [27], FreeSeed [40], DIF-Net [35], DIF-Gaussian [35], and C²RV [36]). The results are reported in Tab. 2. (i) When reconstructing CT volumes from 6, 8, and 10 X-ray projection views, our X-LRM surpasses the SOTA 2D feedforward method, FreeSeed, by 2.12, 1.16, and 1.16 dB in PSNR. Compared to the SOTA 3D feedforward method, C²RV, X-LRM improves the performance by 1.54, 1.41, and 0.37 dB in PSNR, while enjoying over 27 $\times$ faster inference speed. (ii) Unlike previous feedforward methods, X-LRM enjoys better flexibility as it can efficiently reconstruct CT volume with different numbers of input views without training separate models, adapting well to input variations.

Secondly, we compare with three self-supervised methods (NAF [68], R²-Gaussian [69], and SAX-NeRF [8]) and two diffusion-based methods (DiffusionMBIR [10] and DDS [11]). The quantitative results are listed in Tab. 3. Our X-LRM achieves the best overall performance and fastest inference speed. Compared with the second-best method, DiffusionMBIR, our X-LRM is 3.53 dB higher in PSNR. Compared with the second-fastest method, R²-Gaussian, our method is over 2570 $\times$ faster in inference.

Method	Recon.		Left Lung		Right Lung
Method	PSNR	SSIM	DICE	ASD $\downarrow$	DICE	ASD $\downarrow$
NAF	21.91	0.57	48.54	19.14	50.08	9.49
R²-Gaussian	18.58	0.45	29.62	26.12	34.76	12.86
SAX-NeRF	21.83	0.59	39.34	27.55	19.87	20.86
DiffusionMBIR	\ul25.31	\ul0.72	\ul93.10	\ul0.74	\ul93.25	\ul0.67
DDS	23.47	0.53	71.04	2.61	69.58	2.60
X-LRM (Ours)	27.63	0.85	95.60	0.51	95.48	0.48

Table 5: Quantitative lung segmentation results of self-supervised and diffusion-based methods for 6-view reconstructed CTs.

Qualitative Results.

The qualitative results are depicted in Fig. 4 (compared with feedforward methods) and Fig. 5 (compared with self-supervised and diffusion-based methods). As observed from the reconstructed slices, all baseline methods struggle with generating high-quality reconstructions, particularly in sparser-view scenarios. Both feedforward and optimization-based approaches exhibit noticeable blurriness and lack of fine details, leading to incomplete anatomical structures and texture inconsistencies. Structural elements, such as lung regions and organ boundaries, appear unclear, often blending into surrounding areas due to the loss of high-frequency details.

Method	Base Model	+ X-Triplane	+ X-former
PSNR	13.09	28.76	31.33
SSIM	0.42	0.84	0.92

Table 6: Break-down ablation towards higher performance by adding the components of X-LRM. The ablation study is conducted under the 10-view CT reconstruction setting.

In contrast, our X-LRM yields visually sharper reconstructions with well-defined textures and more coherent anatomical structures. Across different view settings, it effectively preserves fine-grained details while maintaining spatial smoothness. Our method consistently reconstructs realistic features with minimal artifacts, demonstrating high-quality performance in extremely sparse-view CT reconstruction.

Application in Segmentation.

We evaluate the reconstructed CT volumes using medical segmentation. We employ the LungMask toolkit [22] to segment the left and right lung from CT reconstructions produced by various methods and compare the results against the ground-truth segmentation obtained from the original CT scans. Specifically, we evaluate lung test data from the 750-test set and 10-test set, testing the corresponding baseline methods and reporting reconstruction performance (PSNR and SSIM) alongside left and right lung segmentation accuracy (DICE and ASD) for 6-view reconstructed volumes. As shown in Tab. 4 and Tab. 5, X-LRM achieves superior reconstruction quality, surpassing C²RV by and DiffusionMBIR by 2.35 and 2.32 dB in PSNR. Additionally, the higher DICE scores and lower ASD values on both the left and right lung indicate that the 3D segmentation on the CT volume reconstructed by X-LRM has a larger overlap and smaller boundary discrepancies with the segmentation mask on the ground-truth CT volume. Fig. 6 shows the visual comparison with four kinds of recent best methods. Both quantitative and qualitative results demonstrate the ability of X-LRM to preserve anatomical structures more accurately and maintain precise shape consistency, surpassing other methods in both reconstruction fidelity and segmentation alignment. These results further highlight the practical advantages of our method.

4.3 Ablation Study

Ablation studies evaluate the effectiveness of the proposed modifications compared to the standard LRM, including X-former and X-triplane. Additionally, we assess the robustness of X-LRM under varying noisy scanning parameters, such as viewing angles, DSD, and DSO. The breakdown study is performed under the 10-view setting, while the robustness analysis is conducted under the 6-view setting.

Noisy parameters			PSNR	SSIM( $10^{-2}$ )
Angles	DSO	DSD	PSNR	SSIM( $10^{-2}$ )
-	-	-	31.05 (-0.00)	91.04 (-0.00)
$\pm 0.5^{\circ}$	-	-	30.93 (-0.12)	90.95 (-0.09)
$\pm 1^{\circ}$	-	-	30.62 (-0.43)	90.71 (-0.33)
-	$\pm 2mm$	-	30.85 (-0.20)	90.89 (-0.15)
-	$\pm 3mm$	-	30.67 (-0.38)	90.73 (-0.31)
-	-	$\pm 2mm$	30.99 (-0.06)	90.99 (-0.05)
-	-	$\pm 3mm$	30.93 (-0.12)	90.95 (-0.09)

Table 7: Ablation study of X-LRM’s robustness to noisy X-ray scanner parameters under a 6-view CT reconstruction setting. We ablate on three parameters: viewing angles, DSO and DSD.

Break-down Ablation.

We adopt the Open-LRM [23] as the base reconstruction model to study the effect of each component of X-LRM towards higher performance. The results of the 10-view reconstruction are reported in Tab. 6. The base model only achieves poor results of 13.09 dB in PSNR. After applying our X-triplane and X-former, the model gains by 15.67 and 2.57 dB in PSNR. These results validate the effectiveness of our proposed methods.

Robustness Analysis.

We conduct a robustness analysis under varying noisy scanning parameters, including viewing angles, source-to-origin distance (DSO), and source-to-detector distance (DSD), using a 6-view reconstruction setting. The introduced noise follows a uniform distribution, modeled as $\eta\sim\mathcal{U}(-\epsilon,+\epsilon)$ . With this noise, the projection images change but the model processes them as if captured under perfect conditions. Tab. 7 shows that X-LRM remains robust to noises of scanning parameters. Viewing angle shifts of $\pm 0.5^{\circ}$ (PSNR -0.12 dB, SSIM -0.0009) and $\pm 1^{\circ}$ results (PSNR -0.43 dB, SSIM -0.0033) have minimal impact on our model. Noises in DSO and DSD only introduce minor effects, with $\pm 3$ mm DSO causing the largest decline (PSNR -0.38 dB, SSIM -0.0031). Despite these fluctuations, performance remains stable, demonstrating the reliability of X-LRM to real-world scanning variations.

5 Conclusion

In this paper, we collect the largest dataset, Torso-16K, to enable large-scale training for CT reconstruction. Torso-16K is over 18× larger than the existing largest benchmark. We propose X-LRM, a Transformer-based feedforward framework consisting of X-former and X-triplane. X-former employs a tokenizer and Transformer backbone to flexibly encode an arbitrary number of input views, enabling X-LRM to reconstruct CT volumes without re-training. X-triplane decodes image tokens into a triplane representation and learns a neural implicit function to model 3D radiodensity. Experiments show that X-LRM surpasses the SOTA 3D feedforward method by 1.5 dB while achieving 27× faster speed, with its application in medical segmentation further highlighting its practical value.

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X-LRM: X-ray Large Reconstruction Model for Extremely Sparse-View Computed Tomography Recovery in One Second