基于亚像素各向异性扩散的低剂量CT重建方法

doi:10.12122/j.issn.1673-4254.2025.01.19

摘要/Abstract

摘要：

目的提出一种基于亚像素各项异性扩散的低剂量CT重建方法。方法通过线性插值技术计算亚像素单元强度值及其二阶差分后，将计算得到的新的梯度信息引入到各项异性扩散过程中，并结合惩罚加权最小二乘模型对低剂量CT投影数据进行滤波，最后使用滤波反投影算法将恢复后的投影数据重建出CT图像。结果在Shepp-Logan体模实验中，与FBP、PWLS-Gibbs和PWLS-TV方法相比，新方法滤波后重建的CT图像在结构相似指数上分别提升了28.13%、5.49%和0.91%，在特征相似指数上分别提升了21.08%、1.78%和1.36%，并且在均方根误差上分别降低了69.59%、18.96%和3.90%。在XCAT体模实验中，与FBP、PWLS-Gibbs和PWLS-TV方法相比，新方法在结构相似指数上分别提高了14.24%、1.43%及7.89%，在特征相似指数上分别提高了9.61%、1.78%及5.66%，同时在均方根误差上分别降低了26.88%、9.41%及18.39%。在临床数据实验中，与FBP、PWLS-Gibbs和PWLS-TV方法重建的CT图像相比，新方法在结构相似指数上分别提升了19.24%、15.63%和3.68%，在特征相似指数上分别提升了4.30%、2.92%和0.43%，同时在均方根误差上分别降低了44.60%、36.84%和15.22%，并且在峰值信噪比上提升至28.39。结论本文提出的新方法可以有效去除低剂量CT图像的噪声和伪影，并可以保持结构细节信息。

关键词: 低剂量CT, 各向异性扩散, 亚像素, 图像重建

Abstract:

Objective We present a new low-dose CT reconstruction method using sub-pixel and anisotropic diffusion. Methods The sub-pixel intensity values and their second-order differences were obtained using linear interpolation techniques, and the new gradient information was then embedded into an anisotropic diffusion process, which was introduced into a penalty-weighted least squares model to reduce the noise in low-dose CT projection data. The high-quality CT image was finally reconstructed using the classical filtered back-projection (FBP) algorithm from the estimated data. Results In the Shepp-Logan phantom experiments, the structural similarity (SSIM) index of the CT image reconstructed by the proposed algorithm, as compared with FBP, PWLS-Gibbs and PWLS-TV algorithms, was increased by 28.13%, 5.49%, and 0.91%, the feature similarity (FSIM) index was increased by 21.08%, 1.78%, and 1.36%, and the root mean square error (RMSE) was reduced by 69.59%, 18.96%, and 3.90%, respectively. In the digital XCAT phantom experiments, the SSIM index of the CT image reconstructed by the proposed algorithm, as compared with FBP, PWLS-Gibbs and PWLS-TV algorithms, was increased by 14.24%, 1.43% and 7.89%, the FSIM index was increased by 9.61%, 1.78% and 5.66%, and the RMSE was reduced by 26.88%, 9.41% and 18.39%, respectively. In clinical experiments, the SSIM index of the image reconstructed using the proposed algorithm was increased by 19.24%, 15.63% and 3.68%, the FSIM index was increased by 4.30%, 2.92% and 0.43%, and the RMSE was reduced by 44.60%, 36.84% and 15.22% in comparison with FBP, PWLS-Gibbs and PWLS-TV algorithms, respectively. Conclusion The proposed method can effectively reduce the noises and artifacts while maintaining the structural details in low-dose CT images.

Key words: low-dose computed tomography, anisotropic diffusion, sub-pixel, image reconstruction

唐诗洲, 苏若兰, 李淑婷, 赖珍珍, 黄进红, 牛善洲. 基于亚像素各向异性扩散的低剂量CT重建方法[J]. 南方医科大学学报, 2025, 45(1): 162-169.

Shizhou TANG, Ruolan SU, Shuting LI, Zhenzhen LAI, Jinhong HUANG, Shanzhou NIU. A low-dose CT reconstruction method using sub-pixel anisotropic diffusion[J]. Journal of Southern Medical University, 2025, 45(1): 162-169.

图/表 13

图1 不同hs下的亚像素

Fig.1 Sub-pixel under different distance hs: (A)hs1; (B)hs1.

图2 数字仿真体模

Fig.2 Digital phantom: Shepp-Logan phantom (A) and XCAT phantom (B).

图3 不同方法重建的Shepp-Logan体模图像

Fig.3 Shepp-Logan images reconstructed by FBP method (A), PWLS-Gibbs method (B), PWLS-TV method (C) and the proposed PWLS-SPAD method (D).

表1 Shepp-Logan体模实验的评估指数

Tab.1 Evaluation indexes of the reconstructed Shepp-Logan images by different methods

Index	FBP	PWLS-Gibbs	PWLS-TV	PWLS-SPAD
SSIM	0.752083	0.913535	0.954934	0.963646
FSIM	0.767575	0.913088	0.916857	0.929354
RMSE	0.111569	0.041859	0.035302	0.033924

图4 Shepp-Logan体模的局部放大图

Fig.4 Zoomed-in views of the reconstructed Shepp-Logan phantom images by FBP method (A), PWLS-Gibbs method (B), PWLS-TV method (C) and the proposed PWLS-SPAD method (D).

表2 图4中ROI的评估指数

Tab.2 Evaluation indexes of the region-of-interest （ROI） in Fig.4

Index	FBP	PWLS-Gibbs	PWLS-TV	PWLS-SPAD
SSIM	0.203666	0.813477	0.850652	0.888047
FSIM	0.399392	0.790398	0.827324	0.853895

图5 不同方法重建的XCAT体模图像

Fig.5 XCAT phantom images reconstructed by FBP method (A), PWLS-Gibbs method (B), PWLS-TV method (C) and the proposed PWLS-SPAD method (D).

表3 XCAT体模实验的评估指数

Tab.3 Evaluation indexes of reconstructed XCAT results by different methods

Index	FBP	PWLS-Gibbs	PWLS-TV	PWLS-SPAD
SSIM	0.793550	0.893789	0.840232	0.906532
FSIM	0.814784	0.877465	0.845212	0.893061
RMSE	0.073716	0.059505	0.066048	0.053903

图6 XCAT体模的局部放大图

Fig.6 Zoomed-in views of the reconstructed XCAT phantom images by FBP method (A), PWLS-Gibbs method (B), PWLS-TV method (C) and the proposed PWLS-SPAD method (D).

表4 图6中ROI的评估指数

Tab.4 Evaluation indexes of ROI in Fig.6

Index	FBP	PWLS-Gibbs	PWLS-TV	PWLS-SPAD
SSIM	0.748943	0.852549	0.798578	0.873204
FSIM	0.806244	0.862104	0.832281	0.867679

表5 低剂量临床数据重建CT图像的评估指数

Tab.5 Evaluation indexes of the reconstructed low-dose clinical CT images by different methods

Index	FBP	PWLS-Gibbs	PWLS-TV	PWLS-SPAD
SSIM	0.795249	0.820050	0.914574	0.948223
FSIM	0.936031	0.948504	0.972051	0.976237
RMSE	0.068670	0.060228	0.044872	0.038042
PSNR	23.26	24.40	26.96	28.39

图8 临床数据重建CT图像的ROI放大图

Fig.8 Zoomed-in views of the ROI in the reconstructed images by FBP method at 400 mAs (A) and 50 mAs (B), by PWLS-Gibbs at 50 mAs (C), by PWLS-TV at 50 mAs (D), and by the proposed PWLS-SPAD method at 50 mAs (E).

表6 图8中ROI的评估指数

Tab.6 Evaluation indexes of ROI in Fig.8

Index	FBP	PWLS-Gibbs	PWLS-TV	PWLS-SPAD
SSIM	0.622500	0.786073	0.783700	0.810993
FSIM	0.840642	0.865528	0.882331	0.919254

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