Image representation affects both the forward model and quantitative feature recovery in model-based iterative CT reconstruction. For isotropically bandlimited signals, the hexagonal lattice is the most sampling-efficient lattice in two dimensions, with greater directional isotropy and a larger alias-free bandwidth than the Cartesian grid at equal density. We develop constant and linear hexagonal projectors for two-dimensional fan-beam CT using box spline calculus. Both bases form a partition of unity on common coefficient centers; the linear tent also reproduces affine functions. We derive analytic ray footprints and effective detector-blur expressions and implement efficient GPU forward and backprojection. On simulated FORBILD data, the linear model improves on Cartesian and hexagonal pixels, with its best noisy-data accuracy at the coarser resolution. Real-world 2DeteCT comparisons use high-dose, high-resolution Cartesian reconstructions as pseudo ground truth and show competitive image and feature agreement. These results establish a practical hexagonal representation for quantitative CT.
Figures & tables
Figure 1: Common hexagonal lattice. Red arrows are translated directions rk forming H-Pixel’s three rhombi; blue arrows are the neighbor directions in Ξl . H-Pixel occupies the shaded central cell; H-Linear’s support is the thin gray outline through neighboring centers.
Figure 2: Common physical regions and error scales for all models. Top: FORBILD truth and absolute errors, n=128 , 300 iterations, seed 2032; truth window [0,0.06] mm -1 , 5-mm bars. Bottom: high-dose MBIR reference and low-dose deviations, 2DeteCT slice 525, n=256 , 100 iterations; reference window [0,0.12] mm -1 , 10-mm bars. Error scales saturate at the shown maxima (mm -1 ).
Model
FORBILD
180 views
450 views
SF
2.75
17.89
84.72
C-Pixel
1.61
18.89
99.86
H-Pixel
2.46
27.00
146.90
H-Linear
2.32
26.94
156.54
Table 1: Independent median forward/backward pair times (ms): 33 synchronized samples per model/geometry. Initialization is separate.
n=128
n=256
Model
Clean
Noisy
Clean
Noisy
SF
26.91
26.40
27.89
21.71
C-Pixel
26.91
26.40
27.89
21.71
H-Pixel
26.97
26.46
27.97
21.80
H-Linear
28.21
27.66
30.52
24.64
Table 2: FORBILD PSNR (dB), 300 iterations for all methods, fixed 5122 evaluation. Clean: intensity-average data; noisy: five paired Poisson seeds. n=128/256 Cartesian coefficient widths have equal-density hexagonal counterparts.
Model
Low dose; n=256
Low dose; n=512
High dose; n=256
High dose; n=512
FO
CM
RL
FO
CM
RL
FO
CM
RL
FO
CM
RL
SF
31.44
18.23
62.84
45.91
25.02
68.81
2.27
9.56
24.09
2.84
8.30
31.56
C-Pixel
31.44
18.23
62.83
45.91
25.02
68.81
2.27
9.56
24.09
2.84
8.30
31.55
H-Pixel
32.08
17.40
50.63
47.19
24.47
58.28
2.26
8.47
24.26
3.02
8.91
31.29
H-Linear
28.42
12.65
32.05
33.82
17.81
56.08
2.44
6.52
18.73
1.83
4.27
18.70
Table 3: 2DeteCT feature deviations (%), 10 bins, three slices, 100 iterations for all methods. n is the Cartesian coefficient-field width; hexagonal grids match cell area. FO/CM/RL are first-order/GLCM/GLRLM family medians. Both doses use the same high-dose MBIR reference; lower is closer agreement.
Image reconstruction recovers images, volumes, or scenes from incomplete, noisy, indirect, or compressed measurements using physical models and learned priors.
Gaussian Splatting (GS) has emerged as a dominating technique for image rendering and has quickly been adapted for the X-ray Computed Tomography (CT) reconstruction task. However, despite its growing popularity, the benefits of GS are typically not substantial enough to motivate a transition from well-established reconstruction algorithms. This paper addresses the most significant remaining limitations of the GS-based approach by introducing FaCT-GS, a framework for fast and flexible CT reconstruction. Enabled by an in-depth optimization of the voxelization and rasterization pipelines, our new method is significantly faster than its predecessors and scales well with projection and output volume size. Furthermore, the improved voxelization enables rapid fitting of Gaussians to pre-existing volumes, which can serve as a prior for warm-starting the reconstruction, or simply as an alternative, compressed representation. FaCT-GS is over 4X faster than the State of the Art GS CT reconstruction on standard 512x512 projections, and over 13X faster on 2k projections. Implementation and data available through: https://github.com/PaPieta/fact-gs.
Pawel Tomasz Pieta, Rasmus Juul Pedersen, Sina Borgi +3
Technical University of Denmark, Kgs. Lyngby, Denmark
Cone-beam computed tomography (CBCT) is widely used for image-guided radiotherapy, but reducing the number of projections to lower dose and scan time makes reconstruction increasingly ill-posed. We present EUReCA (End-to-end Unified REconstruction across Clinical Acquisitions), a geometry-aware feed-forward model for variable-view clinical linac CBCT. For a given acquisition trajectory, EUReCA accepts 8-100 projections with a single set of weights, without view-count-specific retraining; the same architecture and training recipe extend unchanged to other clinical trajectories. It combines learned projection features with an in-frame Feldkamp-Davis-Kress (FDK) reconstruction. The model encodes each projection with a shared multiscale backbone, back-projects features into multiresolution 3D grids using the acquisition geometry, aggregates variable numbers of views at fixed computational cost, and refines the volume with a global 3D transformer and multilevel decoder. On simulated data, EUReCA achieved 29.9-33.2 dB PSNR with 10-100 views and outperformed all applicable feed-forward baselines; it also exceeded iterative optimization-based methods while running orders of magnitude faster. On 15 measured patient CBCT scans evaluated against vendor reconstructions, EUReCA achieved the best performance at every tested view count. These results suggest that geometry-aware, measurement-anchored feed-forward reconstruction can provide a practical and flexible foundation for variable-view linac CBCT.
Jiening Zhu, Chengzhu Zhang, Jason Fan +8
The authors are with the Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY 10065 USA
A long-term goal in CT imaging is to achieve fast and accurate 3D reconstruction from sparse-view projections, thereby reducing radiation exposure, lowering system cost, and enabling timely imaging in clinical workflows. Recent feed-forward approaches have shown strong potential toward this overarching goal, yet their results still suffer from artifacts and loss of fine details. In this work, we introduce Iterative Latent Volumes (ILV), a feed-forward framework that integrates data-driven priors with classical iterative reconstruction principles to overcome key limitations of prior feed-forward models in sparse-view CBCT reconstruction. At its core, ILV constructs an explicit 3D latent volume that is repeatedly updated by conditioning on multi-view X-ray features and the learned anatomical prior, enabling the recovery of fine structural details beyond the reach of prior feed-forward models. In addition, we develop and incorporate several key architectural components, including an X-ray feature volume, group cross-attention, efficient self-attention, and view-wise feature aggregation, that efficiently realize its core latent volume refinement concept. Extensive experiments on a large-scale dataset of approximately 14,000 CT volumes demonstrate that ILV significantly outperforms existing feed-forward and optimization-based methods in both reconstruction quality and speed. These results show that ILV enables fast and accurate sparse-view CBCT reconstruction suitable for clinical use. The project page is available at: https://sngryonglee.github.io/ILV/.