Low-dose CT image reconstruction based on low-rank and total variation joint regularization

doi:10.11772/j.issn.1001-9081.2024040478

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (3): 978-987.DOI: 10.11772/j.issn.1001-9081.2024040478

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Low-dose CT image reconstruction based on low-rank and total variation joint regularization

Yu LIU¹^,², Pengcheng ZHANG¹^,²(), Liyuan ZHANG¹^,², Yi LIU¹^,², Zhiguo GUI¹^,², Xueyi ZHANG¹^,², Chenyifei ZHU¹^,², Haowei TANG¹^,²

^1.Shanxi Provincial Key Laboratory for Biomedical Imaging and Big Data （North University of China），Taiyuan Shanxi 030051，China
^2.School of Information and Communication Engineering，North University of China，Taiyuan Shanxi 030051，China

Received:2024-04-22 Revised:2024-08-28 Accepted:2024-08-30 Online:2024-09-14 Published:2025-03-10
Contact: Pengcheng ZHANG
About author:LIU Yu， born in 1999， M. S. candidate. His research interests include medical image reconstruction， medical image processing.
ZHANG Liyuan， born in 1990， Ph. D.， lecturer. Her research interests include radiotherapy program optimization， medical image processing.
LIU Yi， born in 1987， Ph. D.， professor. Her research interests include medical image analysis， image reconstruction.
GUI Zhiguo， born in 1972， Ph. D.， professor. His research interests include signal and information processing， radiotherapy program optimization， image reconstruction.
ZHANG Xueyi， born in 2000， M. S. candidate. Her research interests include medical image processing， medical image reconstruction.
ZHU Chenyifei， born in 2005. Her research interests include image processing.
TANG Haowei， born in 2000， M. S. candidate. His research interests include image reconstruction.
Supported by:
Shanxi Provincial Basic Research Program(20210302124403);Scientific Research Funding Project for Returned Overseas Students of Shanxi Province(2021-111)

基于低秩与全变分联合正则化的低剂量CT图像重建

刘宇¹^,², 张鹏程¹^,²(), 张丽媛¹^,², 刘祎¹^,², 桂志国¹^,², 张雪怡¹^,², 朱陈一菲¹^,², 汤豪威¹^,²

^1.生物医学成像与影像大数据山西省重点实验室（中北大学），太原 030051
^2.中北大学信息与通信工程学院，太原 030051

通讯作者: 张鹏程
作者简介:刘宇（1999—），男，河北沧州人，硕士研究生，主要研究方向：医学图像重建、医学图像处理
张丽媛（1990—），女，河北石家庄人，讲师，博士，主要研究方向：放射治疗方案优化、医学图像处理
刘祎（1987—），女，河南商丘人，教授，博士，主要研究方向：医学图像分析、图像重建
桂志国（1972—），男，天津人，教授，博士，主要研究方向：信号与信息处理、放射治疗方案优化、图像重建
张雪怡（2000—），女，河南新乡人，硕士研究生，主要研究方向：医学图像处理、医学图像重建
朱陈一菲（2005—），女，河北衡水人，主要研究方向：图像处理
汤豪威（2000—），男，河南周口人，硕士研究生，主要研究方向：图像重建。
基金资助:
山西省基础研究计划项目(20210302124403);山西省回国留学人员科研资助项目(2021?111)

Abstract

Abstract:

Aiming at the problems that the Total Variation （TV） minimization method easily leads to image over-smoothing and block effects in Low-Dose Computed Tomography （LDCT） image reconstruction， an LDCT image reconstruction method based on low-rank and TV joint regularization was proposed to improve the visual quality of LDCT reconstructed images. Firstly， a low-rank and TV joint regularization based image reconstruction model was established， thus， more accurate and natural reconstruction results were obtained theoretically. Secondly， a low-rank prior with non-local self-similarity property was introduced to overcome the limitations of only using the TV minimization method. Finally， the Chambolle-Pock （CP） algorithm was used to optimize and solve the model， which improved the solution efficiency of the model and ensured the effective solution of the model. The effectiveness of the proposed method was verified under three different LDCT scanning conditions. Experimental results on Mayo dataset show that compared with the PWLS-LDMM （Penalized Weighted Least-Squares based on Low-Dimensional Manifold） method， NOWNUNM （NOnlocal Weighted NUclear Norm Minimization） method and CP method， at 25% dose， the proposed method increases the Visual Information Fidelity （VIF） by 28.39%， 8.30% and 2.93%， respectively； at 15% dose， the proposed method increases the VIF by 29.96%， 13.83% and 4.53%， respectively； at 10% dose， the proposed method increases the VIF by 30.22%， 17.10% and 7.66%， respectively. It can be seen that the proposed method can retain more detailed texture information while removing noise and stripe artifacts， which verifies that the proposed method has better noise artifact suppression capability.

Key words: Low-Dose Computed Tomography (LDCT), Chambolle-Pock (CP) algorithm, low-rank, Total Variation (TV), image reconstruction

摘要：

针对全变分（TV）最小化方法在低剂量计算机断层扫描（LDCT）图像重建中易导致的图像过平滑和块状效应等问题，提出一种基于低秩与TV联合正则化的LDCT图像重建方法，以提升LDCT重建图像的视觉质量。首先，建立一个基于低秩与TV联合正则化的图像重建模型，从而从理论上获得更精确和自然的重建结果；其次，通过引入具有非局部自相似特性的低秩先验克服仅使用TV最小化方法存在的局限性；最后，采用Chambolle-Pock （CP）算法优化求解上述模型，以提高模型的求解效率，并保证模型能有效求解。在3种不同LDCT扫描条件下验证所提方法的有效性。在Mayo数据集上的实验结果表明，与PWLS-LDMM（Penalized Weighted Least-Squares based on Low-Dimensional Manifold）方法、NOWNUNM（NOnlocal Weighted NUclear Norm Minimization）方法和CP方法相比，在25%剂量下，所提方法的视觉信息保真度（VIF）分别提升了28.39%、8.30%和2.93%；在15%剂量下，所提方法的VIF分别提升了29.96%、13.83%和4.53%；在10%剂量下，所提方法的VIF分别提升了30.22%、17.10%和7.66%。可见，所提方法在消除噪声和条纹伪影的同时能保留更多的细节纹理信息，验证了所提方法具有较好的噪声伪影抑制能力。

关键词: 低剂量计算机断层扫描, Chambolle-Pock算法, 低秩, 全变分, 图像重建

CLC Number:

TP 391.41

Yu LIU, Pengcheng ZHANG, Liyuan ZHANG, Yi LIU, Zhiguo GUI, Xueyi ZHANG, Chenyifei ZHU, Haowei TANG. Low-dose CT image reconstruction based on low-rank and total variation joint regularization[J]. Journal of Computer Applications, 2025, 45(3): 978-987.

刘宇, 张鹏程, 张丽媛, 刘祎, 桂志国, 张雪怡, 朱陈一菲, 汤豪威. 基于低秩与全变分联合正则化的低剂量CT图像重建[J]. 《计算机应用》唯一官方网站, 2025, 45(3): 978-987.

Figures/Tables 24

References 41

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方法	PSNR/dB	SSIM	RMSE	VIF
FBP	26.829 1	0.521 1	0.045 6	0.422 6
PWLS-LDMM	31.155 3	0.787 5	0.027 7	0.565 7
NOWNUNM	32.395 5	0.803 3	0.024 0	0.579 5
CP	32.939 2	0.798 6	0.022 5	0.550 4
本文方法	33.816 9	0.810 0	0.020 4	0.591 9

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	26.829 1	0.521 1	0.045 6	0.422 6
PWLS-LDMM	31.155 3	0.787 5	0.027 7	0.565 7
NOWNUNM	32.395 5	0.803 3	0.024 0	0.579 5
CP	32.939 2	0.798 6	0.022 5	0.550 4
本文方法	33.816 9	0.810 0	0.020 4	0.591 9

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	26.482 7	0.521 0	0.047 4	0.437 1
PWLS-LDMM	35.885 3	0.861 0	0.016 1	0.642 1
NOWNUNM	35.681 4	0.870 4	0.016 4	0.639 3
CP	35.820 7	0.868 8	0.016 2	0.608 6
本文方法	36.574 2	0.886 5	0.014 8	0.682 4

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	26.482 7	0.521 0	0.047 4	0.437 1
PWLS-LDMM	35.885 3	0.861 0	0.016 1	0.642 1
NOWNUNM	35.681 4	0.870 4	0.016 4	0.639 3
CP	35.820 7	0.868 8	0.016 2	0.608 6
本文方法	36.574 2	0.886 5	0.014 8	0.682 4

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	16.032 9	0.344 4	0.157 9	0.413 1
PWLS-LDMM	32.387 2	0.779 9	0.024 0	0.559 1
NOWNUNM	32.988 0	0.800 3	0.022 4	0.572 0
CP	32.794 8	0.783 3	0.022 9	0.511 1
本文方法	33.594 6	0.811 7	0.020 9	0.577 9

Low-dose CT image reconstruction based on low-rank and total variation joint regularization

基于低秩与全变分联合正则化的低剂量CT图像重建

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Figures/Tables 24

References 41

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Metrics

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	16.237 2	0.316 5	0.154 2	0.432 0
PWLS-LDMM	31.101 1	0.772 9	0.027 9	0.612 3
NOWNUNM	31.349 4	0.779 4	0.027 1	0.675 8
CP	31.312 9	0.955 1	0.027 2	0.700 5
本文方法	33.989 8	0.957 5	0.020 0	0.738 5

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	16.241 8	0.344 4	0.154 1	0.350 3
PWLS-LDMM	31.347 4	0.783 1	0.027 1	0.492 9
NOWNUNM	31.023 7	0.785 4	0.028 1	0.675 0
CP	31.037 3	0.783 3	0.028 1	0.708 6
本文方法	31.442 1	0.811 7	0.026 8	0.753 0

方法	PSNR/dB	SSIM	RMSE	VIF
FBP	14.178 3	0.265 6	0.195 5	0.384 8
PWLS-LDMM	30.411 5	0.758 0	0.030 2	0.617 4
NOWNUNM	30.317 2	0.892 4	0.030 5	0.647 7
CP	31.894 9	0.959 4	0.025 4	0.684 2
本文方法	32.520 8	0.960 5	0.023 7	0.696 7

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方法	25%剂量				15%剂量				10%剂量
方法	PSNR/dB	SSIM	RMSE	VIF	PSNR/dB	SSIM	RMSE	VIF	PSNR/dB	SSIM	RMSE	VIF
FBP	25.206 4	0.523 6	0.054 9	0.368 5	22.703 0	0.445 0	0.073 3	0.331 0	20.585 4	0.383 4	0.093 5	0.298 4
PWLS-LDMM	33.904 7	0.809 7	0.020 1	0.552 9	32.968 5	0.776 7	0.022 4	0.492 7	31.197 7	0.736 6	0.027 5	0.449 0
NOWNUNM	35.127 5	0.855 5	0.017 5	0.655 5	34.237 5	0.827 0	0.019 4	0.562 5	33.410 7	0.799 2	0.021 3	0.499 3
CP	33.718 0	0.856 8	0.020 6	0.689 7	33.580 0	0.841 6	0.020 9	0.612 5	33.023 4	0.822 0	0.022 3	0.543 1
本文方法	35.509 5	0.864 5	0.016 7	0.709 9	34.289 7	0.850 7	0.019 2	0.640 3	33.716 2	0.837 5	0.020 6	0.584 7

方法	25%剂量				15%剂量				10%剂量
方法	PSNR/dB	SSIM	RMSE	VIF	PSNR/dB	SSIM	RMSE	VIF	PSNR/dB	SSIM	RMSE	VIF
FBP	25.206 4	0.523 6	0.054 9	0.368 5	22.703 0	0.445 0	0.073 3	0.331 0	20.585 4	0.383 4	0.093 5	0.298 4
PWLS-LDMM	33.904 7	0.809 7	0.020 1	0.552 9	32.968 5	0.776 7	0.022 4	0.492 7	31.197 7	0.736 6	0.027 5	0.449 0
NOWNUNM	35.127 5	0.855 5	0.017 5	0.655 5	34.237 5	0.827 0	0.019 4	0.562 5	33.410 7	0.799 2	0.021 3	0.499 3
CP	33.718 0	0.856 8	0.020 6	0.689 7	33.580 0	0.841 6	0.020 9	0.612 5	33.023 4	0.822 0	0.022 3	0.543 1
本文方法	35.509 5	0.864 5	0.016 7	0.709 9	34.289 7	0.850 7	0.019 2	0.640 3	33.716 2	0.837 5	0.020 6	0.584 7