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 scarcity of large-scale training datasets and the absence of direct and consistent 3D representations. In this paper, we propose an X-ray Large Reconstruction Model (X-LRM) for extremely sparse-view ($X$-LRM consists of two key components:$X$-former and$X$triplane.$\quad X$-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 largescale dataset comprising over 16 K volume-projection pairs of various torso organs. Extensive experiments demonstrate that X-LRM outperforms the state-of-the-art method by 1.5$d B$and achieves$27 \times$faster speed with better flexibility. Furthermore, the evaluation of lung segmentation tasks also suggests the practical value of our approach. Our code and dataset will be released at https://github.com/Richard-Guofeng-Zhang/X-LRM.

Neural representations (NRs), such as neural fields and 3D Gaussians, effectively model volumetric data in computed tomography (CT) but suffer from severe artifacts under sparse-view settings. To address this, we propose DiffNR, a novel framework that enhances NR optimization with diffusion priors. At its core is SliceFixer, a single-step diffusion model designed to correct artifacts in degraded slices. We integrate specialized conditioning layers into the network and develop tailored data curation strategies to support model finetuning. During reconstruction, SliceFixer periodically generates pseudo-reference volumes, providing auxiliary 3D perceptual supervision to fix underconstrained regions. Compared to prior methods that embed CT solvers into time-consuming iterative denoising, our repair-and-augment strategy avoids frequent diffusion model queries, leading to better runtime performance. Extensive experiments show that DiffNR improves PSNR by 3.99 dB on average, generalizes well across domains, and maintains efficient optimization.

Three-Dimensional Gaussian representation (3DGS) has shown substantial promise in the field of computer vision, but remains unexplored in the field of magnetic resonance imaging (MRI). This study explores its potential for the reconstruction of isotropic resolution 3D MRI from undersampled k-space data. We introduce a novel framework termed 3D Gaussian MRI (3DGSMR), which employs 3D Gaussian distributions as an explicit representation for MR volumes. Experimental evaluations indicate that this method can effectively reconstruct voxelized MR images, achieving a quality on par with that of well-established 3D MRI reconstruction techniques found in the literature. Notably, the 3DGSMR scheme operates under a self-supervised framework, obviating the need for extensive training datasets or prior model training. This approach introduces significant innovations to the domain, notably the adaptation of 3DGS to MRI reconstruction and the novel application of the existing 3DGS methodology to decompose MR signals, which are presented in a complex-valued format.

3D Gaussian splatting (3DGS) has shown promising results in image rendering and surface reconstruction. However, its potential in volumetric reconstruction tasks, such as X-ray computed tomography, remains under-explored. This paper introduces R$^2$-Gaussian, the first 3DGS-based framework for sparse-view tomographic reconstruction. By carefully deriving X-ray rasterization functions, we discover a previously unknown \emph{integration bias} in the standard 3DGS formulation, which hampers accurate volume retrieval. To address this issue, we propose a novel rectification technique via refactoring the projection from 3D to 2D Gaussians. Our new method presents three key innovations: (1) introducing tailored Gaussian kernels, (2) extending rasterization to X-ray imaging, and (3) developing a CUDA-based differentiable voxelizer. Experiments on synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art approaches in accuracy and efficiency. Crucially, it delivers high-quality results in 4 minutes, which is 12$\times$ faster than NeRF-based methods and on par with traditional algorithms.

Aligning two partially-overlapped 3D line reconstructions in Euclidean space is challenging, as we need to simultaneously solve correspondences and relative pose between line reconstructions. This paper proposes a neural network based method and it has three modules connected in sequence: (i) a Multilayer Perceptron (MLP) based network takes Plücker representations of lines as inputs, to extract discriminative line-wise features and matchabilities (how likely each line is going to have a match), (ii) an Optimal Transport (OT) layer takes two-view line-wise features and matchabilities as inputs to estimate a 2D joint probability matrix, with each item describes the matchness of a line pair, and (iii) line pairs with Top-K matching probabilities are fed to a 2-line minimal solver in a RANSAC framework to estimate a six Degree-of-Freedom (6-DoF) rigid transformation. Experiments on both indoor and outdoor datasets show that registration (rotation and translation) precision of our method outperforms baselines significantly.