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CT图像重建滤波器的插值核函数构造法及实例

蒋一鸣1, 邹晶2, 胡晓东2, 赵金涛3   

  1. 1. 江苏科技大学自动化学院, 镇江 212100;
    2. 天津大学精密仪器与光 电子工程学院, 天津 300072;
    3. 天津职业技术师范大学自动化与电气工程学院, 天津 300222
  • 收稿日期:2022-01-29 修回日期:2022-10-23 发布日期:2023-03-29
  • 通讯作者: 赵金涛, Email:zjt2019@tju.edu.cn
  • 基金资助:
    国家自然科学基金面上项目(61771328), 国家重点研发计划(2017YFB1103900)资助课题.

蒋一鸣, 邹晶, 胡晓东, 赵金涛. CT图像重建滤波器的插值核函数构造法及实例[J]. 系统科学与数学, 2023, 43(4): 829-840.

JIANG Yiming, ZOU Jing, HU Xiaodong, ZHAO Jintao. CT Image Reconstruction Filter Design Method by Interpolation Kernel Functions and Examples[J]. Journal of Systems Science and Mathematical Sciences, 2023, 43(4): 829-840.

CT Image Reconstruction Filter Design Method by Interpolation Kernel Functions and Examples

JIANG Yiming1, ZOU Jing2, HU Xiaodong2, ZHAO Jintao3   

  1. 1. School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212100;
    2. School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072;
    3. School of Automation and Electrical Engineering, Tianjin University of Technology and Education, Tianjin 300222
  • Received:2022-01-29 Revised:2022-10-23 Published:2023-03-29
在经典Radon逆变换的基础上, 提出了一种实现Radon逆变换的二阶差商反投影(Second-order Divided-difference Back Projection,SDBP)方法. 对 于离散投影数据,利用插值法将离散的投影值采样序列转化为连续的投影函数, 并根据SDBP公式进一步推导出一种基于插值核函数构造的滤波器设计模型.作为该模型的 应用, 文章套用三角形函数得到了一类新型滤波器.相比传统的滤波器, 新型滤波 器具有调节性能的可控参数,可以根据实际需求增强某些特性, 从而能获得更加理想的重建图像.
Based on the classical inverse Radon transform, the Second-order Divideddifference Back Projection (SDBP) method for realizing inverse Radon transform is proposed in this paper. For discrete projection data, the discrete projection sampling sequence is transformed into continuous projection function by data interpolation. Through logical derivation, a filter design model based on interpolation kernel functions is proposed by using SDBP formula. As an application of the filter design model, a new kind of filter is obtained by applying triangle function. Compared with traditional filters, the new filter has controllable parameters to adjust the performance. Such that some features can be enhanced on the basis of actual needs, so as to obtain better reconstructed images.

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[1] Plessis A D, Roux S, Guelpa A. Comparison of medical and industrial X-ray computed tomography for non-destructive testing. Case Studies in Nondestructive Testing and Evaluation, 2016, 10:17-25.
[2] Buynak C F, Bossi R H. Applied X-ray computed tomography. Nuclear Instruments and Methods in Physics Research Section B:Beam Interactions with Materials and Atoms, 1995, 99(1-4):772- 774.
[3] Plessis A D, Rossouw P. X-ray computed tomography of a titanium aerospace investment casting. Case Studies in Nondestructive Testing and Evaluation, 2015, 3:21-26.
[4] Shi H L, Luo S Q. A novel scheme to design the filter for CT reconstruction using FBP algorithm. Biomedical Engineering Online, 2013, 12:1-15.
[5] Yang M, Yan P, Huang H, et al. Filtered back projection reconstruction research based on Gaussian in PET images. 2012 International Conference on Audio, Language and Image Processing, IEEE, 2012, 360-364.
[6] Wang C, Zhang H, Zeng Z, et al. Application of image reconstruction based on inverse Radon transform in CT system parameter calibration and imaging. Complexity, 2021, 2021:1-10.
[7] Park H S, Lee S M, Kim H P, et al. CT sinogram consistency learning for metal induced beam hardening correction. Medical physics, 2018, 45(12):5376-5384.
[8] Huang H, Tang W, Yang J, et al. Parameters calibration of CT system based on geometric model and inverse Radon transform. 202110th International Conference on Applied Science, Engineering and Technology (ICASET 2021), Atlantis Press, 2021, 113-123.
[9] Gabdrakhmanov I R, Müller D, Teryaev O V. Inverse Radon transform at work. Physics of Particles and Nuclei Letters, 2019, 16(6):625-637.
[10] He J, Wang Y, Ma J. Radon inversion via deep learning. IEEE Transactions on Medical Imaging, 2020, 39(6):2076-2087.
[11] Anikin I V, Szymanowski L. Inverse radon transform and the transverse-momentum dependent functions. Physical Review D, 2019, 100(9):094034.
[12] Willemink M J, Noël P B. The evolution of image reconstruction for CT-From filtered back projection to artificial intelligence. European Radiology, 2019, 29(5):2185-2195.
[13] 杨坪坪, 冯汉升, 许继伟, 等. CT图像重建中的一种新型滤波器. 中国医学物理学杂志, 2021, 38(7):814- 819. (Yang P, Feng H, Xu J, et al. A novel filter for CT image reconstruction. Chinese Journal of Medical Physics, 2021, 38(7):814-819.)
[14] Vincent D J, Hari V S. Edge enhancement and noise smoothening of CT images with anisotropic diffusion filter and unsharp masking. 2018 IEEE Recent Advances in Intelligent Computational Systems (RAICS), IEEE, 2018, 55-59.
[15] 冯聪聪, 宣晓, 高上, 等. 血管造影锥形束CT重建算法中的滤波器设计研究. 中国医学装备, 2020, 17(4):1-4. (Feng C, Xuan X, Gao S, et al. Study on the design of filter in reconstruction algorithm of angiography CBCT. China Medical Equipment, 2020, 17(4):1-4.)
[16] 骆岩红. CT图像重建滤波反投影算法中指数滤波器的研究. 计算机科学, 2014, 41(6A):220-223. (Luo Y. Study on exponential filter of filter back projection algorithm for CT image reconstruction. Computer Science, 2014, 41(6A):220-223.)
[17] Ramachandran G N, Lakshminarayanan A V. Three-dimensional reconstruction from radiographs and electron micrographs:Application of convolutions instead of fourier transforms. Proceedings of the National Academy of Sciences of the United States of America, 1971, 68(9):2236-2240.
[18] Shepp L A, Logan B F. The Fourier reconstruction of a head section. IEEE Transactions on Nuclear Science, 2013, 21(3):21-43.
[19] Ramachandrana G N, Lakshminarayanan A V, Kolaskara A S. Theory of the non-planar peptide unit. Biochimica et Biophysica Acta (BBA)-Protein Structure, 1973, 303(1):8-13.
[20] 翟静, 潘晋孝. 混合滤波函数在FDK算法中的应用. 南昌航空大学学报:自然科学版, 2007, 41(S1):263-266. (Zhai J, Pan J. Application of mixed filter function in FDK algorithm. Journal of Nanchang Hangkong University:Natural Science, 2007, 41(S1):263-266.)
[21] 张斌. 滤波反投影图像重建算法中插值和滤波器研究. 硕士论文. 中北大学, 太原, 2009. (Zhang B. Interpolation and filter research in filter back-projection image reconstruction algorithm. Master Thesis. North University of China, Taiyuan, 2009.)
[22] Wei Y, Wang G, Hsieh J. An intuitive discussion on the ideal ramp filter in computed tomography. Computers and Mathematics with Applications, 2005, 49(5):731-740.
[23] Zhang B, Pan J. A new type of mixed filters for CT image reconstruction. Microcomputer Information, 2009, 25(3):298-308.
[24] Pierzchala P, Kot P. Radon inversion problem for holomorphic functions on circular, strictly convex domains. Complex Analysis and Operator Theory, 2021, 15(4):1-31.
[25] 庄天戈. CT原理与算法. 上海:上海交通大学出版社, 1992. (Zhuang T. CT Principles and Algorithms. Shanghai:Shanghai Jiao Tong University Press, 1992.)
[26] King F W. Hilbert Transforms. Cambridge:Cambridge University Press, 2009.
[27] 乔志伟, 韩焱, 潘晋孝. 解析法图像重建中的理想斜变滤波器的进一步研究. CT理论与应用研究, 2013, 22(1):1-14. (Qiao Z, Han Y, Pan J. A further study on the ideal ramp filter of analytical image reconstruction. Computerized Tomography Theory and Applications, 2013, 22(1):1-14.)
[28] 甘妙格,刘璐瑶. CT图像三维重建体绘制算法重采样改进. 计算机与网络, 2021, 47(8):63-66. (Gan M, Liu L. An improved resampling method for volume rendering algorithm in CT image 3D reconstruction. Computer and Network, 2021, 47(8):63-66.)
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