Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation

Jiang, Yuqi; Mao, Tianyi; Zhou, Jianyong; Zhao, Qile; Yin, Jun; Yi, Xuedong; Wu, Haiyou

doi:10.3390/s25247479

Open AccessArticle

Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation

by

Yuqi Jiang

^1,2,*,

Tianyi Mao

^3,*,

Jianyong Zhou

¹,

Qile Zhao

^4,5,

Jun Yin

¹,

Xuedong Yi

¹ and

Haiyou Wu

¹

The 44th Research Institute of China Electronics Technology Corporation, Chongqing 400060, China

²

The 24th Research Institute of China Electronics Technology Corporation, Chongqing 400060, China

³

College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

⁴

Technology Department of Unmanned Platform System, Xi’an Institute of Applied Optics, Xi’an 710065, China

⁵

Department of Automation, Tsinghua University, Beijing 100081, China

^*

Authors to whom correspondence should be addressed.

Sensors 2025, 25(24), 7479; https://doi.org/10.3390/s25247479

Submission received: 5 September 2025 / Revised: 28 September 2025 / Accepted: 11 November 2025 / Published: 9 December 2025

(This article belongs to the Special Issue Computational Optical Sensing and Imaging)

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Abstract

Coded aperture X-ray computed tomography (CAXCT) measures coded X-ray projections to reconstruct the inner structure of an object. Coded apertures, which determine the point spread function, can be designed to improve the reconstruction quality, but most approaches are computationally expensive, leading to very small images. In this paper, a sparse covariance matrix estimation approach is introduced to minimize the information loss sensed by projections corresponding to large tomographic images. The covariance matrix representing the map of the overlapping information of the projections is obtained by using block matrix multiplication and sparse estimation. A heuristic variant algorithm with a noise factor is presented to search the combinations of D projections leading to maximum non-overlapping information acquisition, where D is the number of unblocking elements on the coded apertures. Numerical experiments with simulated datasets show that the optimization performance of the proposed method is comparable to that of state-of-the-art methods with small images. Further, for the analyzed cases, coded aperture optimization was performed with

512 \times 512

images by analyzing coefficients smaller than

0.02 %

in the covariance matrix.

Keywords: computed tomography; coded aperture; optimization; covariance matrix

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MDPI and ACS Style

Jiang, Y.; Mao, T.; Zhou, J.; Zhao, Q.; Yin, J.; Yi, X.; Wu, H. Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation. Sensors 2025, 25, 7479. https://doi.org/10.3390/s25247479

AMA Style

Jiang Y, Mao T, Zhou J, Zhao Q, Yin J, Yi X, Wu H. Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation. Sensors. 2025; 25(24):7479. https://doi.org/10.3390/s25247479

Chicago/Turabian Style

Jiang, Yuqi, Tianyi Mao, Jianyong Zhou, Qile Zhao, Jun Yin, Xuedong Yi, and Haiyou Wu. 2025. "Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation" Sensors 25, no. 24: 7479. https://doi.org/10.3390/s25247479

APA Style

Jiang, Y., Mao, T., Zhou, J., Zhao, Q., Yin, J., Yi, X., & Wu, H. (2025). Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation. Sensors, 25(24), 7479. https://doi.org/10.3390/s25247479

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Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation

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