基于相对TV最小的CT图像重建算法  

Computed Tomography Reconstruction Algorithm Based on Relative Total Variation Minimization

作　　者：张家浩 乔志伟[1] ZHANG Jiahao;QIAO Zhiwei(School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学计算机与信息技术学院,太原030006

出　　处：《CT理论与应用研究（中英文）》2023年第2期153-169,共17页Computerized Tomography Theory and Applications

基　　金：国家自然科学基金面上项目(模型与数据耦合驱动的快速四维EPRI肿瘤氧成像(62071281));中央引导地方科技发展资金项目(新型TV和学习先验联合约束的快速四维EPRI成像方法(YDZJSX2021A003));山西省回国留学人员科研资助项目(基于新型四维TV正则机理的快速EPRI肿瘤氧成像方法研究(2020-008))。

摘　　要：总变差(TV)最小算法是一种有效的CT图像重建算法,可以对稀疏或含噪投影数据进行高精度重建。然而,在某些情况下,TV算法会产生阶梯状伪影。在图像去噪领域,相对TV算法展现了优于TV算法的性能。鉴于此,将相对TV模型引入图像重建,提出相对TV最小优化模型,并在自适应梯度下降-投影到凸集(ASD-POCS)框架下设计对应的求解算法,以进一步提升重建精度。以Shepp-Logan、FORBILD及真实CT图像仿真模体进行重建实验,验证了该算法的正确性并评估了算法的稀疏重建能力和抗噪能力。实验结果表明,相对TV算法可以实现逆犯罪,可以对稀疏或含噪投影数据进行高精度重建,与TV算法相比,该算法可以取得更高的重建精度。The total variation(TV) minimization algorithm is an effective CT image reconstruction algorithm that can reconstruct sparse or noisy projection data with high accuracy. However, in some cases, the TV algorithm produces stepped artifacts. The relative TV algorithm outperforms TV algorithm in the field of image denoising. In view of this, the relative TV model is introduced into image reconstruction, a relative TV minimum optimization model is proposed, and the corresponding solution algorithm is designed under the framework of adaptive gradient descent projection to the convex set(ASD-POCS) to further improve reconstruction accuracy. The reconstruction experiments were conducted with Shepp Logan, Forbild, and real CT image simulation models to verify the anti-crime ability of the algorithm and evaluate the sparse reconstruction and antinoise abilities of the algorithm. The experimental findings reveal that the algorithm outperforms the TV method in terms of anti-crime capability and the ability to reconstruct sparse or noisy projection data with high precision. Compared with the TV algorithm, the algorithm can achieve higher reconstruction accuracy.

关 键 词：计算机断层成像 相对总变差最小 稀疏重建 ASD-POCS算法 

分 类 号：O242[理学—计算数学] TP391.41[理学—数学]