Hexagonal Basis Projectors for Model-Based Iterative CT Reconstruction

Ke Chen; Alireza Entezari

cs.CVOct 17, 2026

Hexagonal Basis Projectors for Model-Based Iterative CT Reconstruction

Authors: Ke Chen, Alireza Entezari

Organizations: University of Florida

Abstract

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

\vec{r}^{k}

forming H-Pixel’s three rhombi; blue arrows are the neighbor directions in

\Xi^{l}

. 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

512^{2}

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

Image reconstruction recovers images, volumes, or scenes from incomplete, noisy, indirect, or compressed measurements using physical models and learned priors.

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Abstract

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